keywords = {Applications of Nonlinear Dynamics and Chaos Theory,Control and Systems Theory,Control engineering,Mathematical Methods in Physics,Mathematical physics,Mathematical Physics,Physics,Statistical physics,Statistical Physics and Dynamical Systems,System theory,Systems Theory Control},
note = {Introduction -- Analysis of Hybrid Systems -- Singularly Perturbed Systems (SPSs) -- Systems of Dierential Equations with Piecewise Continuous Arguments (EPCA): A Hybrid System Approach -- Reliable Control and State Estimation for Uncertain Impulsive Large-Scale Systems -- Stochastic Hybrid (Impulsive) Systems -- Stochastic Systems with EPCA -- Input-to-State Stability (ISS) for Stochastic Hybrid Systems -- Stability in Terms of Two Measures},
file = {/home/danesabo/Zotero/storage/EKCD8BZX/Alwan and Liu - 2018 - Theory of Hybrid Systems Deterministic and Stocha.pdf}
}
@ -671,8 +670,7 @@ Opportunities and Challenges toward Responsible AI.pdf}
abstract = {We have developed a loop-shaping methodology for robust control design in single-input single-output (SISO) systems with structured and unstructured uncertainties. This design method employs visualization tools that are modifications of the classical Bode plot. Using the proposed method control engineers can easily consider the effects of the structured and unstructured uncertainties without the need for transfer-function models of the plant, the sensitivity function performance, or the uncertainty. The method simultaneously can avoid excessive conservativeness and excessively high order controllers while improving controller performance and robustness. We show utility of the proposed method by applying it to a head-positioning control system in a hard disk drive.},
eventtitle = {{{IEEE Transactions}} on {{Control Systems Technology}}},
file = {/home/danesabo/Zotero/storage/V3Q2EZLG/Atsumi and Messner - 2012 - Modified Bode Plots for Robust Performance in SISO Systems With Structured and Unstructured Uncertai.pdf;/home/danesabo/Zotero/storage/2MYEEYMM/6119239.html}
}
@article{avigadFORMALSYSTEMEUCLID2009,
title = {A {{FORMAL SYSTEM FOR EUCLID}}’{{S}} {{{\emph{ELEMENTS}}}}},
author = {Avigad, Jeremy and Dean, Edward and Mumma, John},
@ -891,7 +907,6 @@ Opportunities and Challenges toward Responsible AI.pdf}
url = {http://arxiv.org/abs/1808.05415},
urldate = {2023-12-12},
abstract = {The reachability semantics for Petri nets can be studied using open Petri nets. For us an "open" Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the outputs of one to the inputs of another. Open Petri nets can be treated as morphisms of a category \$\textbackslash mathsf\{Open\}(\textbackslash mathsf\{Petri\})\$, which becomes symmetric monoidal under disjoint union. However, since the composite of open Petri nets is defined only up to isomorphism, it is better to treat them as morphisms of a symmetric monoidal double category \$\textbackslash mathbb\{O\}\textbackslash mathbf\{pen\}(\textbackslash mathsf\{Petri\})\$. We describe two forms of semantics for open Petri nets using symmetric monoidal double functors out of \$\textbackslash mathbb\{O\}\textbackslash mathbf\{pen\}(\textbackslash mathsf\{Petri\})\$. The first, an operational semantics, gives for each open Petri net a category whose morphisms are the processes that this net can carry out. This is done in a compositional way, so that these categories can be computed on smaller subnets and then glued together. The second, a reachability semantics, simply says which markings of the outputs can be reached from a given marking of the inputs.},
note = {Comment: 30 pages, TikZ figures},
file = {/home/danesabo/Zotero/storage/A7YADSNG/Baez and Master - 2020 - Open Petri Nets.pdf;/home/danesabo/Zotero/storage/4RYR2R52/1808.html}
}
@ -1709,7 +1724,6 @@ Opportunities and Challenges toward Responsible AI.pdf}
url = {http://arxiv.org/abs/2111.11367},
urldate = {2022-03-25},
abstract = {With the proliferation of advanced metering infrastructure (AMI), more real-time data is available to electric utilities and consumers. Such high volumes of data facilitate innovative electricity rate structures beyond flat-rate and time-of-use (TOU) tariffs. One such innovation is real-time pricing (RTP), in which the wholesale market-clearing price is passed directly to the consumer on an hour-by-hour basis. While rare, RTP exists in parts of the United States and has been observed to reduce electric bills. Although these reductions are largely incidental, RTP may represent an opportunity for large-scale peak shaving, demand response, and economic efficiency when paired with intelligent control systems. Algorithms controlling flexible loads and energy storage have been deployed for demand response elsewhere in the literature, but few studies have investigated these algorithms in an RTP environment. If properly optimized, the dynamic between RTP and intelligent control has the potential to counteract the unwelcome spikes and dips of demand driven by growing penetration of distributed renewable generation and electric vehicles (EV). This paper presents a simple reinforcement learning (RL) application for optimal battery control subject to an RTP signal.},
note = {Comment: To be published in the proceedings of the IEEE Power and Energy Society Innovative Smart Grid Technologies (ISGT) Asia Conference},
file = {/home/danesabo/Zotero/storage/HMQGDSL6/Brock et al. - 2021 - An application of reinforcement learning to reside.pdf;/home/danesabo/Zotero/storage/GGP87JEY/2111.html}
}
@ -1754,6 +1768,19 @@ Opportunities and Challenges toward Responsible AI.pdf}
file = {/home/danesabo/Zotero/storage/6VNDBUGU/Brosinsky et al. - 2024 - A Fortunate Decision That You Can Trust Digital T.pdf;/home/danesabo/Zotero/storage/GB3C5QN3/10398577.html}
}
@video{bruntonControlBootcampIntroduction,
entrysubtype = {video},
title = {Control {{Bootcamp}}: {{Introduction}} to {{Robust Control}}},
abstract = {This video motivates robust control with the famous 1978 paper by John Doyle, titled "Guaranteed Margins for LQG Regulators"... Abstract: There are none. C...},
title = {Building the {{Mathematical Library}} of the {{Future}}},
date = {2020-10-01T16:05+00:00},
@ -1929,7 +1956,6 @@ Opportunities and Challenges toward Responsible AI.pdf}
abstract = {In this paper we present a new "external verifier" for the Lean theorem prover, written in Lean itself. This is the first complete verifier for Lean 4 other than the reference implementation in C++ used by Lean itself, and our new verifier is competitive with the original, running between 20\% and 50\% slower and usable to verify all of Lean's mathlib library, forming an additional step in Lean's aim to self-host the full elaborator and compiler. Moreover, because the verifier is written in a language which admits formal verification, it is possible to state and prove properties about the kernel itself, and we report on some initial steps taken in this direction to formalize the Lean type theory abstractly and show that the kernel correctly implements this theory, to eliminate the possibility of implementation bugs in the kernel and increase the trustworthiness of proofs conducted in it. This work is still ongoing but we plan to use this project to help justify any future changes to the kernel and type theory and ensure unsoundness does not sneak in through either the abstract theory or implementation bugs.},
pubstate = {prepublished},
version = {1},
note = {Comment: 17 pages, submitted to ITP 2024},
file = {/home/danesabo/Zotero/storage/JSQM93W8/Carneiro - 2024 - Lean4Lean Towards a formalized metatheory for the.pdf;/home/danesabo/Zotero/storage/DTNS3D35/2403.html}
}
@ -2371,8 +2397,7 @@ Opportunities and Challenges toward Responsible AI.pdf}
abstract = {The application of neutron noise analysis (NNA) to the ex-core neutron detector signal for monitoring the vibration characteristics of a reactor core support barrel (CSB) was investigated. Ex-core flux data were generated by using a nonanalog Monte Carlo neutron transport method in a simulated CSB model where the implicit capture and Russian roulette technique were utilized. First and third order beam and shell modes of CSB vibration were modeled based on parallel processing simulation. A NNA module was developed to analyze the ex-core flux data based on its time variation, normalized power spectral density, normalized cross-power spectral density, coherence, and phase differences. The data were then analyzed with a fuzzy logic module to determine the vibration characteristics. The ex-core neutron signal fluctuation was directly proportional to the CSB's vibration observed at 8~Hz and 15~Hz in the beam mode vibration, and at 8~Hz in the shell mode vibration. The coherence result between flux pairs was unity at the vibration peak frequencies. A distinct pattern of phase differences was observed for each of the vibration models. The developed fuzzy logic module demonstrated successful recognition of the vibration frequencies, modes, orders, directions, and phase differences within 0.4~ms for the beam and shell mode vibrations.},
note = {G704-000135.2015.47.2.004}
abstract = {The application of neutron noise analysis (NNA) to the ex-core neutron detector signal for monitoring the vibration characteristics of a reactor core support barrel (CSB) was investigated. Ex-core flux data were generated by using a nonanalog Monte Carlo neutron transport method in a simulated CSB model where the implicit capture and Russian roulette technique were utilized. First and third order beam and shell modes of CSB vibration were modeled based on parallel processing simulation. A NNA module was developed to analyze the ex-core flux data based on its time variation, normalized power spectral density, normalized cross-power spectral density, coherence, and phase differences. The data were then analyzed with a fuzzy logic module to determine the vibration characteristics. The ex-core neutron signal fluctuation was directly proportional to the CSB's vibration observed at 8~Hz and 15~Hz in the beam mode vibration, and at 8~Hz in the shell mode vibration. The coherence result between flux pairs was unity at the vibration peak frequencies. A distinct pattern of phase differences was observed for each of the vibration models. The developed fuzzy logic module demonstrated successful recognition of the vibration frequencies, modes, orders, directions, and phase differences within 0.4~ms for the beam and shell mode vibrations.}
}
@article{cimattiSMTBasedVerificationHybrid2021,
@ -2569,6 +2594,13 @@ Opportunities and Challenges toward Responsible AI.pdf}
file = {/home/danesabo/Zotero/storage/H2VIPJCV/Conti et al. - 2022 - Side-channel attacks on mobile and IoT devices for.pdf}
}
@online{ControlCOVID19System,
title = {Control of {{COVID-19}} System Using a Novel Nonlinear Robust Control Algorithm - {{ScienceDirect}}},
title = {Convergence: {{Facilitating Transdisciplinary Integration}} of {{Life Sciences}}, {{Physical Sciences}}, {{Engineering}}, and {{Beyond}}},
shorttitle = {Convergence},
@ -2644,7 +2683,7 @@ Opportunities and Challenges toward Responsible AI.pdf}
}
@misc{CPS-def,
note = {Definition from National Science Foundation, 2016, “Cyber-Physical Systems,” program solicitation 16-549, NSF document number nsf16549, March 4. https://www.nsf.gov/publications/pub\_summ.jsp?ods\_key=nsf16549}
type = {misc}
}
@article{cremersFormalMethodsSecurity2003,
@ -2735,8 +2774,7 @@ NTRS Research Center: Langley Research Center (LaRC)},
}
@misc{Cyber-X,
date = {2020-08/2022-02},
note = {The University of Pittsburgh team has conducted customer discovery interviews with stakeholders in cybersecurity, the Industrial Internet of Things, operational technology, and various verticals, including the energy sector. This discovery has included over 80 interviews with stakeholders in the cybersecurity of operational technology.}
date = {2020-08/2022-02}
}
@online{CyberAttackGerman2015,
@ -3062,7 +3100,6 @@ NTRS Research Center: Langley Research Center (LaRC)},
urldate = {2023-10-05},
abstract = {We show that diffusion models can achieve image sample quality superior to the current state-of-the-art generative models. We achieve this on unconditional image synthesis by finding a better architecture through a series of ablations. For conditional image synthesis, we further improve sample quality with classifier guidance: a simple, compute-efficient method for trading off diversity for fidelity using gradients from a classifier. We achieve an FID of 2.97 on ImageNet 128\$\textbackslash times\$128, 4.59 on ImageNet 256\$\textbackslash times\$256, and 7.72 on ImageNet 512\$\textbackslash times\$512, and we match BigGAN-deep even with as few as 25 forward passes per sample, all while maintaining better coverage of the distribution. Finally, we find that classifier guidance combines well with upsampling diffusion models, further improving FID to 3.94 on ImageNet 256\$\textbackslash times\$256 and 3.85 on ImageNet 512\$\textbackslash times\$512. We release our code at https://github.com/openai/guided-diffusion},
pubstate = {prepublished},
note = {Comment: Added compute requirements, ImageNet 256\$\textbackslash times\$256 upsampling FID and samples, DDIM guided sampler, fixed typos},
file = {/home/danesabo/Zotero/storage/AI9WPMRK/Dhariwal and Nichol - 2021 - Diffusion Models Beat GANs on Image Synthesis.pdf;/home/danesabo/Zotero/storage/LVTW6CH8/2105.html}
}
@ -3149,6 +3186,24 @@ NTRS Research Center: Langley Research Center (LaRC)},
abstract = {This paper deals with a robust fault-detection and isolation (FDI) technique, which is applied to the traction system of an electric vehicle, in the presence of structured and unstructured uncertainties. Due to the structural and multidomain properties of the bond graph, the generation of a nonlinear model and residuals for the studied system with adaptive thresholds is synthesized. The parameters and structured uncertainties are identified by using a least-square algorithm. A super-twisting observer is used to estimate both unstructured uncertainties and unknown inputs. Cosimulation with real experimental data shows the robustness of the residuals to the considered uncertainties and their sensitivity to the faults.},
eventtitle = {{{IEEE Transactions}} on {{Vehicular Technology}}},
file = {/home/danesabo/Zotero/storage/BPDWU2H7/Djeziri et al. - 2009 - Robust Monitoring of an Electric Vehicle With Structured and Unstructured Uncertainties.pdf}
}
@online{DoDCyberWorkforce,
title = {{{DoD Cyber Workforce Framework}} – {{DoD Cyber Exchange}}},
url = {https://public.cyber.mil/wid/dcwf/},
@ -3183,6 +3238,33 @@ NTRS Research Center: Langley Research Center (LaRC)},
title = {2020 {{ICS Cybersecurity Year}} in {{Review}} | {{Dragos}}},
date = {2021-02-24T12:29:00Z},
@ -3250,7 +3332,6 @@ NTRS Research Center: Langley Research Center (LaRC)},
abstract = {A goal of artificial intelligence is to construct an agent that can solve a wide variety of tasks. Recent progress in text-guided image synthesis has yielded models with an impressive ability to generate complex novel images, exhibiting combinatorial generalization across domains. Motivated by this success, we investigate whether such tools can be used to construct more general-purpose agents. Specifically, we cast the sequential decision making problem as a text-conditioned video generation problem, where, given a text-encoded specification of a desired goal, a planner synthesizes a set of future frames depicting its planned actions in the future, after which control actions are extracted from the generated video. By leveraging text as the underlying goal specification, we are able to naturally and combinatorially generalize to novel goals. The proposed policy-as-video formulation can further represent environments with different state and action spaces in a unified space of images, which, for example, enables learning and generalization across a variety of robot manipulation tasks. Finally, by leveraging pretrained language embeddings and widely available videos from the internet, the approach enables knowledge transfer through predicting highly realistic video plans for real robots.},
abstract = {Microstructure reconstruction, a major component of inverse computational materials engineering, is currently advancing at an unprecedented rate. While various training-based and training-free approaches are developed, the majority of contributions are based on generative adversarial networks. In contrast, diffusion models constitute a more stable alternative, which have recently become the new state of the art and currently attract much attention. The present work investigates the applicability of diffusion models to the reconstruction of real-world microstructure data. For this purpose, a highly diverse and morphologically complex data set is created by combining and processing databases from the literature, where the reconstruction of realistic micrographs for a given material class demonstrates the ability of the model to capture these features. Furthermore, a fiber composite data set is used to validate the applicability of diffusion models to small data set sizes that can realistically be created by a single lab. The quality and diversity of the reconstructed microstructures is quantified by means of descriptor-based error metrics as well as the Fréchet inception distance (FID) score. Although not present in the training data set, the generated samples are visually indistinguishable from real data to the untrained eye and various error metrics are computed. This demonstrates the utility of diffusion models in microstructure reconstruction and provides a basis for further extensions such as 2D-to-3D reconstruction or application to multiscale modeling and structure–property linkages.},
abstract = {Control of wire-borne underactuated brachiating robots requires a robust feedback control design that can deal with dynamic uncertainties, actuator constraints and unmeasurable states. In this paper, we develop a robust feedback control for brachiating on flexible cables, building on previous work on optimal trajectory generation and time-varying LQR controller design. We propose a novel simplified model for approximation of the flexible cable dynamics, which enables inclusion of parametric model uncertainties in the system. We then use semidefinite programming (SDP) and sum-of-squares (SOS) optimization to synthesize a time-varying feedback control with formal robustness guarantees to account for model uncertainties and unmeasurable states in the system. Through simulation, hardware experiments and comparison with a time-varying LQR controller, it is shown that the proposed robust controller results in relatively large robust backward reachable sets and is able to reliably track a pre-generated optimal trajectory and achieve the desired brachiating motion in the presence of parametric model uncertainties, actuator limits, and unobservable states.},
eventtitle = {2020 {{IEEE}}/{{RSJ International Conference}} on {{Intelligent Robots}} and {{Systems}} ({{IROS}})},
file = {/home/danesabo/Zotero/storage/7WJD7TUD/Farzan et al. - 2020 - Robust Control Synthesis and Verification for Wire-Borne Underactuated Brachiating Robots Using Sum-.pdf;/home/danesabo/Zotero/storage/JGNKK6F7/9341348.html}
}
@article{faselEnsembleSINDyRobustSparse2022,
title = {Ensemble-{{SINDy}}: {{Robust}} Sparse Model Discovery in the Low-Data, High-Noise Limit, with Active Learning and Control},
abstract = {COVID-19 has been a worldwide concern since the outbreak. Many strategies have been involved such as suppression and mitigation strategies to deal with this epidemic. In this paper, a new mathematical-engineering strategy is introduced in order to control the COVID-19 epidemic. Thereby, control theory is involved in controlling the unstable epidemic alongside with the other suggested strategies until the vaccine will hopefully be invented as soon as possible. A new robust control algorithm is introduced to compensate the COVID-19 nonlinear system by propose a proper controller after using necessary assumptions and analysis are made. In addition, the Variable Transformation Technique (VTT) is used to simplify the COVID-19 system. Furthermore, the Most Valuable Player Algorithm (MVPA) is applied in order to optimize the parameters of the proposed controller. The simulation results are based on the daily reports of two cities Hubei (China) and Lazio (Italy) since the outbreak. It can be concluded that the proposed control algorithm can effectively compensate the COVID-19 system. In addition, it can be considered as an effective mathematical-engineering strategy to control this epidemic alongside with the other strategies.},
keywords = {Coronavirus,COVID-19,Most Valuable Player Algorithm,Nonlinear system,Robust control algorithm,Variable Transformation Technique}
}
@article{hahnAUTOMATEDCYBERSECURITY,
title = {{{AUTOMATED CYBER SECURITY TESTING PLATFORM FOR INDUSTRIAL CONTROL SYSTEMS}}},
author = {Hahn, Andrew and Sandoval, Daniel R and Fasano, Raymond E and Lamb, Christopher},
@ -4707,6 +4864,24 @@ Regulatory Premises.pdf}
file = {/home/danesabo/Zotero/storage/M9EPIB2N/Hailesellasie and Hasan - 2018 - Intrusion Detection in PLC-Based Industrial Contro.pdf}
}
@article{hamiltonjr.RobustControllerDesign1997,
title = {Robust {{Controller Design}} and {{Experimental Verification}} of {{I}}.c. {{Engine Speed Control}}},
author = {Hamilton Jr., G. Kent and Franchek, Matthew A.},
date = {1997},
journaltitle = {International Journal of Robust and Nonlinear Control},
volume = {7},
number = {6},
pages = {609--627},
issn = {1099-1239},
doi = {10.1002/(SICI)1099-1239(199706)7:6<609::AID-RNC294>3.0.CO;2-1},
file = {/home/danesabo/Zotero/storage/XZLUUDTS/Hamilton Jr. and Franchek - 1997 - Robust Controller Design and Experimental Verification of I.c. Engine Speed Control.pdf}
}
@report{hancockIncorporationThermalHydraulic2021,
title = {Incorporation of {{Thermal Hydraulic Models}} for {{Thermal Power Dispatch}} into a {{PWR Power Plant Simulator}}},
author = {Hancock, Stephen G. and Westover, Tyler L. and Luo, Yusheng},
@ -5001,7 +5176,6 @@ Regulatory Premises.pdf}
urldate = {2023-10-05},
abstract = {Classifier guidance is a recently introduced method to trade off mode coverage and sample fidelity in conditional diffusion models post training, in the same spirit as low temperature sampling or truncation in other types of generative models. Classifier guidance combines the score estimate of a diffusion model with the gradient of an image classifier and thereby requires training an image classifier separate from the diffusion model. It also raises the question of whether guidance can be performed without a classifier. We show that guidance can be indeed performed by a pure generative model without such a classifier: in what we call classifier-free guidance, we jointly train a conditional and an unconditional diffusion model, and we combine the resulting conditional and unconditional score estimates to attain a trade-off between sample quality and diversity similar to that obtained using classifier guidance.},
pubstate = {prepublished},
note = {Comment: A short version of this paper appeared in the NeurIPS 2021 Workshop on Deep Generative Models and Downstream Applications: https://openreview.net/pdf?id=qw8AKxfYbI},
eventtitle = {Conference on {{Decision}} and {{Control}}},
isbn = {978-0-7803-3590-5 978-0-7803-3591-2 978-0-7803-3592-9 978-0-7803-3593-6},
langid = {english},
note = {IEEE catalog number 96CH35989, 96CB35989}
langid = {english}
}
@online{InteractionRoundoffNoise,
@ -5452,8 +5624,7 @@ Regulatory Premises.pdf}
}
@misc{IT-def,
date = {2021},
note = {Definition from National Institute of Standards and Technology: “Information Technology: any equipment or interconnected system or subsystem of equipment that is used in the automatic acquisition, storage, manipulation, management, movement, control, display, switching, interchange, transmission, or reception of data or information by the executive agency.”}
date = {2021}
}
@inproceedings{jackyPyModelModelbasedTesting2011,
@ -5710,7 +5881,6 @@ Regulatory Premises.pdf}
abstract = {This work develops a methodology for creating a data-driven digital twin from a library of physics-based models representing various asset states. The digital twin is updated using interpretable machine learning. Specifically, we use optimal trees---a recently developed scalable machine learning method---to train an interpretable data-driven classifier. Training data for the classifier are generated offline using simulated scenarios solved by the library of physics-based models. These data can be further augmented using experimental or other historical data. In operation, the classifier uses observational data from the asset to infer which physics-based models in the model library are the best candidates for the updated digital twin. The approach is demonstrated through the development of a structural digital twin for a 12ft wingspan unmanned aerial vehicle. This digital twin is built from a library of reduced-order models of the vehicle in a range of structural states. The data-driven digital twin dynamically updates in response to structural damage or degradation and enables the aircraft to replan a safe mission accordingly. Within this context, we study the performance of the optimal tree classifiers and demonstrate how their interpretability enables explainable structural assessments from sparse sensor measurements, and also informs optimal sensor placement.},
file = {/home/danesabo/Zotero/storage/ACPJQ3GN/Kapteyn and Willcox - 2020 - From Physics-Based Models to Predictive Digital Tw.pdf}
}
@ -6018,7 +6188,6 @@ Regulatory Premises.pdf}
urldate = {2023-10-05},
abstract = {How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions are two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.},
pubstate = {prepublished},
note = {Comment: Fixes a typo in the abstract, no other changes},
abstract = {In this work, we propose DiffWave, a versatile diffusion probabilistic model for conditional and unconditional waveform generation. The model is non-autoregressive, and converts the white noise signal into structured waveform through a Markov chain with a constant number of steps at synthesis. It is efficiently trained by optimizing a variant of variational bound on the data likelihood. DiffWave produces high-fidelity audios in different waveform generation tasks, including neural vocoding conditioned on mel spectrogram, class-conditional generation, and unconditional generation. We demonstrate that DiffWave matches a strong WaveNet vocoder in terms of speech quality (MOS: 4.44 versus 4.43), while synthesizing orders of magnitude faster. In particular, it significantly outperforms autoregressive and GAN-based waveform models in the challenging unconditional generation task in terms of audio quality and sample diversity from various automatic and human evaluations.},
pubstate = {prepublished},
version = {3},
keywords = {Audio and Speech Processing (eess.AS),Computation and Language (cs.CL),FOS: Computer and information sciences,FOS: Electrical engineering electronic engineering information engineering,Machine Learning (cs.LG),Machine Learning (stat.ML),Sound (cs.SD)},
note = {\subsection{Other}
ICLR 2021 (oral)}
keywords = {Audio and Speech Processing (eess.AS),Computation and Language (cs.CL),FOS: Computer and information sciences,FOS: Electrical engineering electronic engineering information engineering,Machine Learning (cs.LG),Machine Learning (stat.ML),Sound (cs.SD)}
abstract = {Increasing volatilities within power transmission and distribution force power grid operators to amplify their use of communication infrastructure to monitor and control their grid. The resulting increase in communication creates a larger attack surface for malicious actors. Indeed, cyber attacks on power grids have already succeeded in causing temporary, large-scale blackouts in the recent past. In this paper, we analyze the communication infrastructure of power grids to derive resulting fundamental challenges of power grids with respect to cybersecurity. Based on these challenges, we identify a broad set of resulting attack vectors and attack scenarios that threaten the security of power grids. To address these challenges, we propose to rely on a defense-in-depth strategy, which encompasses measures for (i) device and application security, (ii) network security, (iii) physical security, as well as (iv) policies, procedures, and awareness. For each of these categories, we distill and discuss a comprehensive set of state-of-the art approaches, and identify further opportunities to strengthen cybersecurity in interconnected power grids.},
keywords = {DGC read},
note = {Comment: 19 pages, 2 figures, 1 table},
file = {/home/danesabo/Zotero/storage/4G3A2ZG6/Krause et al. - 2021 - Cybersecurity in Power Grids Challenges and Oppor.pdf;/home/danesabo/Zotero/storage/6M69ML7H/2105.html}
}
@ -6304,7 +6469,6 @@ ICLR 2021 (oral)}
abstract = {In today’s world, critical infrastructure is often controlled by computing systems. This introduces new risks for cyber attacks, which can compromise the security and disrupt the functionality of these systems. It is therefore necessary to build such systems with strong guarantees of resiliency against cyber attacks. One way to achieve this level of assurance is using formal verification, which provides proofs of system compliance with desired cyber security properties. The use of Formal Methods (FM) in aspects of cyber security and safety-critical systems are reviewed in this article. We split FM into the three main classes: theorem proving, model checking and lightweight FM. To allow the different uses of FM to be compared, we define a common set of terms. We further develop categories based on the type of computing system FM are applied in. Solutions in each class and category are presented, discussed, compared and summarised. We describe historical highlights and developments and present a state-of-the-art review in the area of FM in cyber security. This review is presented from the point of view of FM practitioners and researchers, commenting on the trends in each of the classes and categories. This is achieved by considering all types of FM, several types of security and safety critical systems and by structuring the taxonomy accordingly. The article hence provides a comprehensive overview of FM and techniques available to system designers of security-critical systems, simplifying the process of choosing the right tool for the task. The article concludes by summarising the discussion of the review, focusing on best practices, challenges, general future trends and directions of research within this field.},
langid = {english},
pubstate = {prepublished},
note = {Comment: Technical Report, Long survey version},
file = {/home/danesabo/Zotero/storage/DE5L3BKT/Kulik et al. - 2021 - A Survey of Practical Formal Methods for Security.pdf}
}
@ -6454,6 +6618,19 @@ ICLR 2021 (oral)}
file = {/home/danesabo/Zotero/storage/NC537RQV/Kyoung-Dae Kim and Kumar - 2012 - Cyber–Physical Systems A Perspective at the Cente.pdf}
}
@book{lamarshIntroductionNuclearEngineering2018,
title = {Introduction to Nuclear Engineering},
author = {Lamarsh, John R. and Baratta, Anthony John},
date = {2018},
edition = {Fourth edition},
publisher = {Pearson Education},
location = {Hoboken},
isbn = {978-0-13-457005-1},
langid = {english},
pagetotal = {802},
file = {/home/danesabo/Zotero/storage/NRS6A7PT/Lamarsh and Baratta - 2018 - Introduction to nuclear engineering.pdf}
}
@article{langFormalVerificationApplied,
title = {Formal {{Verification Applied}} to {{Autonomous Spacecraft Attitude Control}}},
author = {Lang, Kendra and Klett, Corbin and Hawkins, Kelsey and Feron, Eric and Tsiotras, Panagiotis and Phillips, Sean},
abstract = {Formal verification tools are cited as an essential component to enable more widespread development and adoption of advanced autonomous systems. While numerous techniques and tools exist, the applicability of these tools to actual systems under development is currently uncertain. There are myriad reasons for such uncertainty, mostly stemming from assumptions necessary for such tools to work, such as: 1) The assumption that an underlying dynamics model or Simulink model is available, 2) The assumption that the dynamics are low-dimensional, 3) The assumption that the dynamics are linear or linearizable without sacrificing accuracy, and 4) The assumption that the underlying controllers and autonomy algorithms are available and easily modeled. This paper first presents a novel satellite benchmark that incorporates autonomous switching between multiple modes of operation related to attitude control. The result is a hybrid system with nonlinear rotational dynamics restricted to a manifold within each mode. Several open source verification tools are then applied to this benchmark to determine any results that can be drawn about the stability of the overall system. We provide a thorough comparison and discussion of the benefits and drawbacks of those tools we tested, none of which were capable of completely verifying stability requirements over the entire benchmark to the best of our efforts. We also discuss the significant hurdles that remain to implementing these tools on realistic autonomous systems, and the techniques we have found to be the most applicable. The contributions of this paper are: 1) a challenging benchmark on which developers can test their verification tools, and 2) a useful starting point to anyone who wants to apply formal methods to autonomous aerospace systems and to advance the conversation on what remains to be accomplished for these tools to be of practical use.},
note = {Generated from Scopus record by KAUST IRTS on 2021-02-18},
file = {/home/danesabo/Zotero/storage/3VGFTA43/Lang et al. - 2021 - Formal verification applied to autonomous spacecra.pdf}
}
@ -6683,8 +6859,7 @@ for defect classification of TFT–LCD panels.pdf}
location = {Hoboken},
isbn = {978-0-470-63349-6},
pagetotal = {540},
keywords = {DAS Get from Library},
note = {Static optimization -- Optimal control of discrete-time systems -- Optimal control of continuous-time systems -- The tracking problem and other lqr extensions -- Final-time-free and constrained input control -- Dynamic programming -- Optimal control for polynomial systems -- Output feedback and structured control -- Robustness and multivariable frequency-domain techniques -- Differential games -- Reinforcement learning and optimal adaptive control}
keywords = {DAS Get from Library}
}
@article{liDynamicBayesianNetwork2017,
@ -6808,7 +6983,6 @@ for defect classification of TFT–LCD panels.pdf}
urldate = {2024-08-08},
abstract = {Programmable Logic Controllers (PLC) are widely used for industrial automation including safety systems at CERN. The incorrect behaviour of the PLC control system logic can cause significant financial losses by damage of property or the environment or even injuries in some cases, therefore ensuring their correct behaviour is essential. While testing has been for many years the traditional way of validating the PLC control system logic, CERN developed a model checking platform to go one step further and formally verify PLC logic. This platform, called PLCverif, first released internally for CERN usage in 2019, is now available to anyone since September 2020 via an open source licence. In this paper, we will first give an overview of the PLCverif platform capabilities before focusing on the improvements done since 2019 such as the larger support coverage of the Siemens PLC programming languages, the better support of the C Bounded Model Checker backend (CBMC) and the process of releasing PLCverif as an open-source software.},
note = {Comment: 18th International Conference on Accelerator and Large Experimental Physics Control Systems (ICALEPCS2021)},
file = {/home/danesabo/Zotero/storage/XAG39WDC/Lopez-Miguel et al. - 2022 - PLCverif Status of a Formal Verification Tool for.pdf;/home/danesabo/Zotero/storage/AKP5GGFY/2203.html}
}
@ -6866,7 +7040,6 @@ for defect classification of TFT–LCD panels.pdf}
abstract = {Interpreting predictions from tree ensemble methods such as gradient boosting machines and random forests is important, yet feature attribution for trees is often heuristic and not individualized for each prediction. Here we show that popular feature attribution methods are inconsistent, meaning they can lower a feature’s assigned importance when the true impact of that feature actually increases. This is a fundamental problem that casts doubt on any comparison between features. To address it we turn to recent applications of game theory and develop fast exact tree solutions for SHAP (SHapley Additive exPlanation) values, which are the unique consistent and locally accurate attribution values. We then extend SHAP values to interaction effects and define SHAP interaction values. We propose a rich visualization of individualized feature attributions that improves over classic attribution summaries and partial dependence plots, and a unique “supervised” clustering (clustering based on feature attributions). We demonstrate better agreement with human intuition through a user study, exponential improvements in run time, improved clustering performance, and better identification of influential features. An implementation of our algorithm has also been merged into XGBoost and LightGBM, see http://github.com/slundberg/shap for details.},
langid = {english},
pubstate = {prepublished},
note = {Comment: Follow-up to 2017 ICML Workshop arXiv:1706.06060},
file = {/home/danesabo/Zotero/storage/IX57CTJX/Lundberg et al. - 2019 - Consistent Individualized Feature Attribution for .pdf}
}
@ -6882,10 +7055,24 @@ for defect classification of TFT–LCD panels.pdf}
abstract = {Understanding why a model makes a certain prediction can be as crucial as the prediction’s accuracy in many applications. However, the highest accuracy for large modern datasets is often achieved by complex models that even experts struggle to interpret, such as ensemble or deep learning models, creating a tension between accuracy and interpretability. In response, various methods have recently been proposed to help users interpret the predictions of complex models, but it is often unclear how these methods are related and when one method is preferable over another. To address this problem, we present a unified framework for interpreting predictions, SHAP (SHapley Additive exPlanations). SHAP assigns each feature an importance value for a particular prediction. Its novel components include: (1) the identification of a new class of additive feature importance measures, and (2) theoretical results showing there is a unique solution in this class with a set of desirable properties. The new class unifies six existing methods, notable because several recent methods in the class lack the proposed desirable properties. Based on insights from this unification, we present new methods that show improved computational performance and/or better consistency with human intuition than previous approaches.},
langid = {english},
pubstate = {prepublished},
note = {Comment: To appear in NIPS 2017},
file = {/home/danesabo/Zotero/storage/NGGDHXKJ/Lundberg and Lee - 2017 - A Unified Approach to Interpreting Model Predictio.pdf}
}
@book{lynchDynamicalSystemsApplications2018,
title = {Dynamical {{Systems}} with {{Applications}} Using {{Python}}},
author = {Lynch, Stephen},
date = {2018},
edition = {1},
publisher = {Springer International Publishing},
location = {Cham},
doi = {10.1007/978-3-319-78145-7},
abstract = {Dynamical Systems with Applications using Python},
isbn = {978-3-319-78145-7},
langid = {english},
keywords = {Applications of Mathematics,Complex Systems,Dynamical Systems and Ergodic Theory,Dynamics,Mathematical and Computational Engineering,Mathematical Physics and Mathematics,Mathematics,Mathematics and Statistics,Mathematics. Analysis,Ordinary Differential Equations,Python (Computer program language),Statistical Physics and Dynamical Systems},
title = {Regions of Robust Relative Stability for {{PI}} Controllers and {{LTI}} Plants with Unstructured Multiplicative Uncertainty: {{A}} Second-Order-Based Example},
shorttitle = {Regions of Robust Relative Stability for {{PI}} Controllers and {{LTI}} Plants with Unstructured Multiplicative Uncertainty},
author = {Matušů, Radek and Senol, Bilal and Pekař, Libor},
file = {/home/danesabo/Zotero/storage/6JTZB7BD/Matušů et al. - 2023 - Regions of robust relative stability for PI controllers and LTI plants with unstructured multiplicat.pdf}
}
@article{mazeikaMBSEsecModelBasedSystems2020,
title = {{{MBSEsec}}: {{Model-Based Systems Engineering Method}} for {{Creating Secure Systems}}},
shorttitle = {{{MBSEsec}}},
@ -7303,7 +7511,6 @@ for defect classification of TFT–LCD panels.pdf}
langid = {english},
pagetotal = {501},
keywords = {DAS Get from Library},
note = {Literaturverz. S. 486 - 488},
file = {/home/danesabo/Zotero/storage/LRYF79TY/Michel et al. - 2008 - Stability of dynamical systems continuous, discon.pdf}
}
@ -7489,22 +7696,6 @@ Insights from the Social Sciences.pdf}
abstract = {All models are wrong, but some are useful. —George E. P. Box ~ Model-Based Systems Engineering MBSE is the application of modeling systems as a cost-effective way to explore and document system characteristics. By testing and validating system characteristics early, models facilitate timely learning of properties and behaviors, enabling fast feedback on requirements and design decisions. Models provide an efficient way to explore, update, and communicate system aspects to stakeholders while significantly reducing or eliminating dependence on traditional documents. MBSERead more},
@ -7561,8 +7752,7 @@ The Digital Transformation of the Product Management Process: Conception of Digi
author = {Montalvo Martín, Cristina and Pázsit, Imre and Nylén, Henrik},
date = {2012},
publisher = {E.T.S.I. Minas (UPM)},
abstract = {Surveillance of core barrel vibrations has been performed in the Swedish Ringhals PWRs for several years. This surveillance is focused mainly on the pendular motion of the core barrel, which is known as the beam mode. The monitoring of the beam mode has suggested that its amplitude increases along the cycle and decreases after refuelling. In the last 5 years several measurements have been taken in order to understand this behaviour. Besides, a non-linear fitting procedure has been implemented in order to better distinguish the different components of vibration. By using this fitting procedure, two modes of vibration have been identified in the frequency range of the beam mode. Several results coming from the trend analysis performed during these years indicate that one of the modes is due to the core barrel motion itself and the other is due to the individual flow induced vibrations of the fuel elements. In this work, the latest results of this monitoring are presented.},
abstract = {Surveillance of core barrel vibrations has been performed in the Swedish Ringhals PWRs for several years. This surveillance is focused mainly on the pendular motion of the core barrel, which is known as the beam mode. The monitoring of the beam mode has suggested that its amplitude increases along the cycle and decreases after refuelling. In the last 5 years several measurements have been taken in order to understand this behaviour. Besides, a non-linear fitting procedure has been implemented in order to better distinguish the different components of vibration. By using this fitting procedure, two modes of vibration have been identified in the frequency range of the beam mode. Several results coming from the trend analysis performed during these years indicate that one of the modes is due to the core barrel motion itself and the other is due to the individual flow induced vibrations of the fuel elements. In this work, the latest results of this monitoring are presented.}
}
@online{Montreat360App2022,
@ -8052,7 +8242,6 @@ The Digital Transformation of the Product Management Process: Conception of Digi
urldate = {2023-10-05},
abstract = {Diffusion models have recently been shown to generate high-quality synthetic images, especially when paired with a guidance technique to trade off diversity for fidelity. We explore diffusion models for the problem of text-conditional image synthesis and compare two different guidance strategies: CLIP guidance and classifier-free guidance. We find that the latter is preferred by human evaluators for both photorealism and caption similarity, and often produces photorealistic samples. Samples from a 3.5 billion parameter text-conditional diffusion model using classifier-free guidance are favored by human evaluators to those from DALL-E, even when the latter uses expensive CLIP reranking. Additionally, we find that our models can be fine-tuned to perform image inpainting, enabling powerful text-driven image editing. We train a smaller model on a filtered dataset and release the code and weights at https://github.com/openai/glide-text2im.},
pubstate = {prepublished},
note = {Comment: 20 pages, 18 figures},
file = {/home/danesabo/Zotero/storage/3J4B8WWE/Nichol et al. - 2022 - GLIDE Towards Photorealistic Image Generation and.pdf;/home/danesabo/Zotero/storage/9D62GJKI/2112.html}
}
@ -8183,7 +8372,6 @@ The Digital Transformation of the Product Management Process: Conception of Digi
abstract = {In this article, we discuss a novel education approach to control theory in undergraduate engineering programs. In particular, we elaborate on the inclusion of an introductory course on process control during the first years of the program, to appear right after the students undergo basic calculus and physics courses. Our novel teaching proposal comprises debating the basic elements of control theory without requiring any background on advanced mathematical frameworks from the part of the students. The methodology addresses, conceptually, the majority of the steps required for the analysis and design of simple control systems. Herein, we thoroughly detail this educational guideline, as well as tools that can be used in the classroom. Furthermore, we propose a cheap test-bench kit and an open-source numerical simulator that can be used to carry out experiments during the proposed course. Most importantly, we also assess on how the Introduction to process control course has affected the undergraduate program on Control and Automation Engineering at Universidade Federal de Santa Catarina (UFSC, Brazil). Specifically, we debate the outcomes of implementing our education approach at UFSC from 2016 to 2023, considering students' rates of success in other control courses and perspectives on how the chair helped them throughout the course of their program. Based on randomised interviews, we indicate that our educational approach has had good teaching-learning results: students tend to be more motivated for other control-related subjects, while exhibiting higher rates of success.},
langid = {english},
pubstate = {prepublished},
note = {Comment: 55 pages, 13 figures, Screening at the Journal of Control, Automation and Electrical Systems},
file = {/home/danesabo/Zotero/storage/LT33TIEF/Normey-Rico and Morato - 2023 - Teaching control with Basic Maths Introduction to.pdf}
}
@ -8200,8 +8388,7 @@ The Digital Transformation of the Product Management Process: Conception of Digi
}
@misc{NSF,
date = {2016-03-04},
note = {Definition from National Science Foundation, “Cyber-Physical Systems,” program solicitation 16-549, https://www.nsf.gov/publications/pub\_summ.jsp?ods\_key=nsf16549}
date = {2016-03-04}
}
@online{NUARIAddressingNational,
@ -8504,8 +8691,7 @@ The Digital Transformation of the Product Management Process: Conception of Digi
}
@misc{OT-def,
date = {2021},
note = {Definition from National Institute of Standards and Technology: “Operational Technology: programmable systems or devices that interact with the physical environment (or manage devices that interact with the physical environment). These systems/devices detect or cause a direct change through the monitoring and/or control of devices, processes, and events. Examples include industrial control systems, building management systems, fire control systems, and physical access control mechanisms.”}
date = {2021}
}
@article{oudinaModelingTrustCyberPhysical2023,
@ -9170,7 +9356,6 @@ The Digital Transformation of the Product Management Process: Conception of Digi
urldate = {2024-03-07},
abstract = {We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original mathematical terms -- might be addressable via generation from language models. We present an automated prover and proof assistant, GPT-f, for the Metamath formalization language, and analyze its performance. GPT-f found new short proofs that were accepted into the main Metamath library, which is to our knowledge, the first time a deep-learning based system has contributed proofs that were adopted by a formal mathematics community.},
pubstate = {prepublished},
note = {Comment: 15+5 pages},
file = {/home/danesabo/Zotero/storage/DYZKP6NH/Polu and Sutskever - 2020 - Generative Language Modeling for Automated Theorem.pdf;/home/danesabo/Zotero/storage/IQP2QELV/2009.html}
}
@ -9547,7 +9732,6 @@ The Digital Transformation of the Product Management Process: Conception of Digi
abstract = {The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.},
pubstate = {prepublished},
keywords = {diffusion models},
note = {Comment: Proceedings of the 32nd International Conference on Machine Learning},
file = {/home/danesabo/Zotero/storage/AFW2WCSS/Rezende and Mohamed - 2016 - Variational Inference with Normalizing Flows.pdf;/home/danesabo/Zotero/storage/GEBQP5TR/1505.html}
}
@ -9697,7 +9881,6 @@ The Digital Transformation of the Product Management Process: Conception of Digi
urldate = {2023-10-05},
abstract = {By decomposing the image formation process into a sequential application of denoising autoencoders, diffusion models (DMs) achieve state-of-the-art synthesis results on image data and beyond. Additionally, their formulation allows for a guiding mechanism to control the image generation process without retraining. However, since these models typically operate directly in pixel space, optimization of powerful DMs often consumes hundreds of GPU days and inference is expensive due to sequential evaluations. To enable DM training on limited computational resources while retaining their quality and flexibility, we apply them in the latent space of powerful pretrained autoencoders. In contrast to previous work, training diffusion models on such a representation allows for the first time to reach a near-optimal point between complexity reduction and detail preservation, greatly boosting visual fidelity. By introducing cross-attention layers into the model architecture, we turn diffusion models into powerful and flexible generators for general conditioning inputs such as text or bounding boxes and high-resolution synthesis becomes possible in a convolutional manner. Our latent diffusion models (LDMs) achieve a new state of the art for image inpainting and highly competitive performance on various tasks, including unconditional image generation, semantic scene synthesis, and super-resolution, while significantly reducing computational requirements compared to pixel-based DMs. Code is available at https://github.com/CompVis/latent-diffusion .},
pubstate = {prepublished},
note = {Comment: CVPR 2022},
file = {/home/danesabo/Zotero/storage/52SBVWJ7/Rombach et al. - 2022 - High-Resolution Image Synthesis with Latent Diffus.pdf;/home/danesabo/Zotero/storage/ID2GIIZ3/2112.html}
abstract = {We present a new method for learning control law that stabilizes an unknown nonlinear dynamical system at an equilibrium point. We formulate a system identification task in a self-supervised learning setting that jointly learns a controller and corresponding stable closed-loop dynamics hypothesis. The input-output behavior of the unknown dynamical system under random control inputs is used as the supervising signal to train the neural network-based system model and the controller. The proposed method relies on the Lyapunov stability theory to generate a stable closed-loop dynamics hypothesis and corresponding control law. We demonstrate our method on various nonlinear control problems such as n-link pendulum balancing and trajectory tracking, pendulum on cart balancing, and wheeled vehicle path following.},
keywords = {Computer Science - Machine Learning,Computer Science - Robotics,Electrical Engineering and Systems Science - Systems and Control},
note = {Comment: Copyright 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works},
file = {/home/danesabo/Zotero/storage/DYHN77BB/Saha et al. - 2021 - Neural Identification for Control.pdf;/home/danesabo/Zotero/storage/ERWUWG8S/2009.html}
abstract = {We propose a technique for producing ‘visual explanations’ for decisions from a large class of Convolutional Neural Network (CNN)-based models, making them more transparent and explainable.},
langid = {english},
note = {Comment: This version was published in International Journal of Computer Vision (IJCV) in 2019; A previous version of the paper was published at International Conference on Computer Vision (ICCV'17)},
file = {/home/danesabo/Zotero/storage/ZCYUH685/Selvaraju et al. - 2020 - Grad-CAM Visual Explanations from Deep Networks v.pdf)}
}
@book{senameRobustControlLinear2013,
title = {Robust {{Control}} and {{Linear Parameter Varying Approaches}}: {{Application}} to {{Vehicle Dynamics}}},
shorttitle = {Robust {{Control}} and {{Linear Parameter Varying Approaches}}},
editor = {Sename, Olivier and Gaspar, Peter and Bokor, József},
date = {2013},
series = {Lecture {{Notes}} in {{Control}} and {{Information Sciences}}},
file = {/home/danesabo/Zotero/storage/J46HBD3C/Sename et al. - 2013 - Robust Control and Linear Parameter Varying Approaches Application to Vehicle Dynamics.pdf}
abstract = {Modern engineering systems include many components of different types and functions. Verifying that these systems satisfy given specifications can be an arduous task, as most formal verification methods are limited to systems of moderate size. Recently, contract theory has been proposed as a modular framework for defining specifications. In this paper, we present a contract theory for discrete-time dynamical control systems relying on assume/guarantee contracts, which prescribe assumptions on the input of the system and guarantees on the output. We then focus on contracts defined by linear constraints, and develop efficient computational tools for verification of satisfaction and refinement based on linear programming. We exemplify these tools in a simulation example, proving a certain safety specification for a two-vehicle autonomous driving setting.},
langid = {english},
pubstate = {prepublished},
note = {Comment: 9 pages, 5 figures},
file = {/home/danesabo/Zotero/storage/KYZMWWB7/Sharf et al. - 2021 - AssumeGuarantee Contracts for Dynamical Systems .pdf}
abstract = {Explaining the output of a deep network remains a challenge. In the case of an image classifier, one type of explanation is to identify pixels that strongly influence the final decision. A starting point for this strategy is the gradient of the class score function with respect to the input image. This gradient can be interpreted as a sensitivity map, and there are several techniques that elaborate on this basic idea. This paper makes two contributions: it introduces SMOOTHGRAD, a simple method that can help visually sharpen gradient-based sensitivity maps, and it discusses lessons in the visualization of these maps. We publish the code for our experiments and a website with our results.},
langid = {english},
pubstate = {prepublished},
note = {Comment: 10 pages},
file = {/home/danesabo/Zotero/storage/32ADXEX3/Smilkov et al. - 2017 - SmoothGrad removing noise by adding noise.pdf}
abstract = {Denoising diffusion probabilistic models (DDPMs) have achieved high quality image generation without adversarial training, yet they require simulating a Markov chain for many steps to produce a sample. To accelerate sampling, we present denoising diffusion implicit models (DDIMs), a more efficient class of iterative implicit probabilistic models with the same training procedure as DDPMs. In DDPMs, the generative process is defined as the reverse of a Markovian diffusion process. We construct a class of non-Markovian diffusion processes that lead to the same training objective, but whose reverse process can be much faster to sample from. We empirically demonstrate that DDIMs can produce high quality samples \$10 \textbackslash times\$ to \$50 \textbackslash times\$ faster in terms of wall-clock time compared to DDPMs, allow us to trade off computation for sample quality, and can perform semantically meaningful image interpolation directly in the latent space.},
pubstate = {prepublished},
note = {Comment: ICLR 2021; updated connections with ODEs at page 6, fixed some typos in the proof},
abstract = {We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on low-dimensional manifolds, we perturb the data with different levels of Gaussian noise, and jointly estimate the corresponding scores, i.e., the vector fields of gradients of the perturbed data distribution for all noise levels. For sampling, we propose an annealed Langevin dynamics where we use gradients corresponding to gradually decreasing noise levels as the sampling process gets closer to the data manifold. Our framework allows flexible model architectures, requires no sampling during training or the use of adversarial methods, and provides a learning objective that can be used for principled model comparisons. Our models produce samples comparable to GANs on MNIST, CelebA and CIFAR-10 datasets, achieving a new state-of-the-art inception score of 8.87 on CIFAR-10. Additionally, we demonstrate that our models learn effective representations via image inpainting experiments.},
pubstate = {prepublished},
note = {Comment: NeurIPS 2019 (Oral)},
file = {/home/danesabo/Zotero/storage/92EXAJWP/Song and Ermon - 2020 - Generative Modeling by Estimating Gradients of the.pdf;/home/danesabo/Zotero/storage/EPN682ZV/1907.html}
abstract = {Score-based generative models can produce high quality image samples comparable to GANs, without requiring adversarial optimization. However, existing training procedures are limited to images of low resolution (typically below 32x32), and can be unstable under some settings. We provide a new theoretical analysis of learning and sampling from score models in high dimensional spaces, explaining existing failure modes and motivating new solutions that generalize across datasets. To enhance stability, we also propose to maintain an exponential moving average of model weights. With these improvements, we can effortlessly scale score-based generative models to images with unprecedented resolutions ranging from 64x64 to 256x256. Our score-based models can generate high-fidelity samples that rival best-in-class GANs on various image datasets, including CelebA, FFHQ, and multiple LSUN categories.},
pubstate = {prepublished},
note = {Comment: NeurIPS 2020},
file = {/home/danesabo/Zotero/storage/6YZT8E6Q/Song and Ermon - 2020 - Improved Techniques for Training Score-Based Gener.pdf;/home/danesabo/Zotero/storage/585R6E4V/2006.html}
abstract = {Wiring diagrams, as seen in digital circuits, can be nested hierarchically and thus have an aspect of self-similarity. We show that wiring diagrams form the morphisms of an operad \$\textbackslash mcT\$, capturing this self-similarity. We discuss the algebra \$\textbackslash Rel\$ of mathematical relations on \$\textbackslash mcT\$, and in so doing use wiring diagrams as a graphical language with which to structure queries on relational databases. We give the example of circuit diagrams as a special case. We move on to show how plug-and-play devices and also recursion can be formulated in the operadic framework as well. Throughout we include many examples and figures.},
pubstate = {prepublished},
note = {Comment: 28 pages},
file = {/home/danesabo/Zotero/storage/T5BKJJFT/Spivak - 2013 - The operad of wiring diagrams formalizing a graph.pdf;/home/danesabo/Zotero/storage/LWDRTFCD/1305.html}
abstract = {Here we show an example of why it can be a very bad idea to invert some plant dynamics, for example with unstable eigenvalues, for loop shaping. Code available at: faculty.washington.edu/sbrunton/control\_bootcamp\_code.zip These lectures follow Chapters 1 \& 3 from: Machine learning control, by Duriez, Brunton, \& Noack https://www.amazon.com/Machine-Learni... Chapters available at: http://faculty.washington.edu/sbrunto... This video was produced at the University of Washington}
abstract = {This video motivates robust control with the famous 1978 paper by John Doyle, titled "Guaranteed Margins for LQG Regulators"... Abstract: There are none. Code available at: faculty.washington.edu/sbrunton/control\_bootcamp\_code.zip These lectures follow Chapters 1 \& 3 from: Machine learning control, by Duriez, Brunton, \& Noack https://www.amazon.com/Machine-Learni... Chapters available at: http://faculty.washington.edu/sbrunto... This video was produced at the University of Washington}
abstract = {This video describes some of the fundamental limitations of robustness, including time delays and right-half plane zeros. Code available at: faculty.washington.edu/sbrunton/control\_bootcamp\_code.zip These lectures follow Chapters 1 \& 3 from: Machine learning control, by Duriez, Brunton, \& Noack https://www.amazon.com/Machine-Learni... Chapters available at: http://faculty.washington.edu/sbrunto... This video was produced at the University of Washington}
abstract = {Here we show that peaks in the sensitivity function result in a lack of robustness. Code available at: faculty.washington.edu/sbrunton/control\_bootcamp\_code.zip These lectures follow Chapters 1 \& 3 from: Machine learning control, by Duriez, Brunton, \& Noack https://www.amazon.com/Machine-Learni... Chapters available at: http://faculty.washington.edu/sbrunto... This video was produced at the University of Washington}
abstract = {The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power systems. Physics-Informed Neural Networks (PINNs) have recently emerged as a promising solution for drastically accelerating computations of non-linear dynamical systems. This work investigates the applicability of these methods for power system dynamics, focusing on the dynamic response to load disturbances. Comparing the prediction of PINNs to the solution of conventional solvers, we find that PINNs can be 10 to 1000 times faster than conventional solvers. At the same time, we find them to be sufficiently accurate and numerically stable even for large time steps. To facilitate a deeper understanding, this paper also present a new regularisation of Neural Network (NN) training by introducing a gradient-based term in the loss function. The resulting NNs, which we call dtNNs, help us deliver a comprehensive analysis about the strengths and weaknesses of the NN based approaches, how incorporating knowledge of the underlying physics affects NN performance, and how this compares with conventional solvers for power system dynamics.},
keywords = {Computer Science - Machine Learning,Electrical Engineering and Systems Science - Systems and Control},
note = {Comment: Published in Electric Power Systems Research},
file = {/home/danesabo/Zotero/storage/B5YWLZSE/Stiasny and Chatzivasileiadis - 2023 - Physics-Informed Neural Networks for Time-Domain S.pdf;/home/danesabo/Zotero/storage/6GUKX8Z6/2303.html}
abstract = {We explore the possibility to use physics-informed neural networks to drastically accelerate the solution of ordinary differential-algebraic equations that govern the power system dynamics. When it comes to transient stability assessment, the traditionally applied methods either carry a significant computational burden, require model simplifications, or use overly conservative surrogate models. Conventional neural networks can circumvent these limitations but are faced with high demand of high-quality training datasets, while they ignore the underlying governing equations. Physics-informed neural networks are different: they incorporate the power system differential algebraic equations directly into the neural network training and drastically reduce the need for training data. This paper takes a deep dive into the performance of physics-informed neural networks for power system transient stability assessment. Introducing a new neural network training procedure to facilitate a thorough comparison, we explore how physics-informed neural networks compare with conventional differential-algebraic solvers and classical neural networks in terms of computation time, requirements in data, and prediction accuracy. We illustrate the findings on the Kundur two-area system, and assess the opportunities and challenges of physics-informed neural networks to serve as a transient stability analysis tool, highlighting possible pathways to further develop this method.},
pubstate = {prepublished},
keywords = {Computer Science - Machine Learning,Electrical Engineering and Systems Science - Systems and Control},
note = {Comment: 9 pages, 8 figures},
file = {/home/danesabo/Zotero/storage/J8WQK82B/Stiasny et al. - 2023 - Transient Stability Analysis with Physics-Informed.pdf;/home/danesabo/Zotero/storage/BFZKZ9EM/2106.html}
abstract = {Programmable Logic Controllers (PLCs) play a critical role in the industrial control systems. Vulnerabilities in PLC programs might lead to attacks causing devastating consequences to the critical infrastructure, as shown in Stuxnet and similar attacks. In recent years, we have seen an exponential increase in vulnerabilities reported for PLC control logic. Looking back on past research, we found extensive studies explored control logic modification attacks, as well as formal verification-based security solutions.},
file = {/home/danesabo/Zotero/storage/T9L6LJMI/Sun et al. - 2021 - SoK Attacks on Industrial Control Logic and Forma.pdf;/home/danesabo/Zotero/storage/VSLPZVKJ/Sun et al. - 2021 - SoK Attacks on Industrial Control Logic and Forma.pdf;/home/danesabo/Zotero/storage/4KZGCWIW/2006.html}
abstract = {An adaptive robust controller (ARC) has been recently developed for read/write head embedded control systems of hard disk drives (HDDs). This structure is applicable to both track seeking and track following modes, and it makes the mode switching control algorithms found in conventional HDD servosystems unnecessary. An Improved Desired Compensation ARC (IDCARC) scheme is proposed in this paper, in which the traditional ARC is powered by a dynamic adaptive term. In this approach the adaptation regressor is calculated using reference trajectory information. Moreover, a robust analysis of this method is developed, in which a controller designed based on a simple model of the system is verified in a closed loop performance of a more comprehensive model of the system. The simulation result verifies the significant improvement of the performance of IDCARC compared to that of ARC and its robustness for this model. It is observed that in the presence of large disturbances the proposed method preserves the stability and a suitable performance while the ARC fails even in stability.},
eventtitle = {{{IEEE Transactions}} on {{Industrial Electronics}}},
keywords = {Adaptive control,Adaptive robust control,Control systems,dynamic adaptation,hard disk drive,hard disk drive (HDD),Hard disks,nonlinear robust control,Performance analysis,Power system modeling,Programmable control,Robust control,Robustness,robustness verification,Servosystems,Stability},
file = {/home/danesabo/Zotero/storage/ZZ54H786/Taghirad and Jamei - 2008 - Robust Performance Verification of Adaptive Robust Controller for Hard Disk Drives.pdf}
abstract = {In this paper, we use the language of operads to study open dynamical systems. More specifically, we study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones. The syntactic architecture of such interconnections is encoded using the visual language of wiring diagrams. We define the symmetric monoidal category W, from which we may construct an operad O(W), whose objects are black boxes with input and output ports, and whose morphisms are wiring diagrams, thus prescribing the algebraic rules for interconnection. We then define two W-algebras, G and L, which associate semantic content to the structures in W. Respectively, they correspond to general and to linear systems of differential equations, in which an internal state is controlled by inputs and produces outputs. As an example, we use these algebras to formalize the classical problem of systems of tanks interconnected by pipes, and hence make explicit the algebraic relationships among systems at different levels of granularity.},
pubstate = {prepublished},
note = {Comment: 26 pages},
file = {/home/danesabo/Zotero/storage/T2V4TXP6/Vagner et al. - 2015 - Algebras of Open Dynamical Systems on the Operad o.pdf;/home/danesabo/Zotero/storage/R4GV5EVF/1408.html}
abstract = {In this paper, we use the language of operads to study open dynamical systems. More specifically, we study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones. The syntactic architecture of such interconnections is encoded using the visual language of wiring diagrams. We define the symmetric monoidal category W, from which we may construct an operad O(W), whose objects are black boxes with input and output ports, and whose morphisms are wiring diagrams, thus prescribing the algebraic rules for interconnection. We then define two W-algebras, G and L, which associate semantic content to the structures in W. Respectively, they correspond to general and to linear systems of differential equations, in which an internal state is controlled by inputs and produces outputs. As an example, we use these algebras to formalize the classical problem of systems of tanks interconnected by pipes, and hence make explicit the algebraic relationships among systems at different levels of granularity.},
pubstate = {prepublished},
note = {Comment: 26 pages},
file = {/home/danesabo/Zotero/storage/HQBVBU8A/Vagner et al. - 2015 - Algebras of Open Dynamical Systems on the Operad o.pdf;/home/danesabo/Zotero/storage/HJFNVTGE/1408.html}
abstract = {Natural hazards, such as earthquakes and strong wind events, place large forces on tall, slender structures and on long-span bridges. In view of the numerous uncertainties due to model errors, stress calculations, material properties, and environmental ...},
abstract = {Two applications of a noise diagnostic methodology were performed using ex-core neutron detector data from a pressurized water reactor (PWR). A feedback dynamics model of the neutron power spectral density (PSD) was derived from a low-order whole-plant physical model made stochastic using the Langevin technique. From a functional fit to plant data, the response of the dynamic system to changes in important physical parameters was evaluated by a direct sensitivity analysis. In addition, changes in monitored spectra were related to changes in physical parameters and detection thresholds using common surveillance discriminants were determined. A resonance model was developed from perturbation theory to give the ex-core neutron detector response for small in-core mechanical motions in terms of a pole-strength factor, a resonance asymmetry (or skewness) factor, a vibration damping factor, and a frequency of vibration. The mechanical motion parameters for several resonances were determined by a functional fit of the model to plant data taken at various times during a fuel cycle and were tracked to determine trends that indicated vibrational changes of reactor internals. In addition, the resonance model gave the ability to separate the resonant components of the PSD after the parameters had been identified. As a result, the behavior of several vibration peaks were monitored over a fuel cycle. 9 refs., 6 figs., 1 tab.},
note = {AC05-84OR21400}
abstract = {Two applications of a noise diagnostic methodology were performed using ex-core neutron detector data from a pressurized water reactor (PWR). A feedback dynamics model of the neutron power spectral density (PSD) was derived from a low-order whole-plant physical model made stochastic using the Langevin technique. From a functional fit to plant data, the response of the dynamic system to changes in important physical parameters was evaluated by a direct sensitivity analysis. In addition, changes in monitored spectra were related to changes in physical parameters and detection thresholds using common surveillance discriminants were determined. A resonance model was developed from perturbation theory to give the ex-core neutron detector response for small in-core mechanical motions in terms of a pole-strength factor, a resonance asymmetry (or skewness) factor, a vibration damping factor, and a frequency of vibration. The mechanical motion parameters for several resonances were determined by a functional fit of the model to plant data taken at various times during a fuel cycle and were tracked to determine trends that indicated vibrational changes of reactor internals. In addition, the resonance model gave the ability to separate the resonant components of the PSD after the parameters had been identified. As a result, the behavior of several vibration peaks were monitored over a fuel cycle. 9 refs., 6 figs., 1 tab.}
title = {Diffusion {{Models}}: {{A Comprehensive Survey}} of {{Methods}} and {{Applications}}},
shorttitle = {Diffusion {{Models}}},
author = {Yang, Ling and Zhang, Zhilong and Song, Yang and Hong, Shenda and Xu, Runsheng and Zhao, Yue and Zhang, Wentao and Cui, Bin and Yang, Ming-Hsuan},
date = {2023-11-09},
journaltitle = {ACM Comput. Surv.},
volume = {56},
number = {4},
pages = {105:1--105:39},
issn = {0360-0300},
doi = {10.1145/3626235},
url = {https://doi.org/10.1145/3626235},
urldate = {2024-10-01},
abstract = {Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview of the rapidly expanding body of work on diffusion models, categorizing the research into three key areas: efficient sampling, improved likelihood estimation, and handling data with special structures. We also discuss the potential for combining diffusion models with other generative models for enhanced results. We further review the wide-ranging applications of diffusion models in fields spanning from computer vision, natural language processing, temporal data modeling, to interdisciplinary applications in other scientific disciplines. This survey aims to provide a contextualized, in-depth look at the state of diffusion models, identifying the key areas of focus and pointing to potential areas for further exploration. Github:},
file = {/home/danesabo/Zotero/storage/2U7R7BKF/Yang et al. - 2023 - Diffusion Models A Comprehensive Survey of Methods and Applications.pdf}
}
@article{yangDiffusionModelsComprehensive2024,
title = {Diffusion {{Models}}: {{A Comprehensive Survey}} of {{Methods}} and {{Applications}}},
abstract = {Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive uncertainty estimates for 10 common inference methods on both regression and classification tasks. Our experiments demonstrate that commonly used metrics (e.g. test log-likelihood) can be misleading. Our experiments also indicate that inference innovations designed to capture structure in the posterior do not necessarily produce high quality posterior approximations.},
note = {Comment: Accepted to ICML UDL 2019},
file = {/home/danesabo/Zotero/storage/3STLFSLA/Yao et al. - 2019 - Quality of Uncertainty Quantification for Bayesian.pdf;/home/danesabo/Zotero/storage/KKA3FIX8/1906.html}
abstract = {Digital Twins (DT) are essentially Dynamic Data-driven models that serve as real-time symbiotic “virtual replicas” of real-world systems. DT can leverage fundamentals of Dynamic Data-Driven Applications Systems (DDDAS) bidirectional symbiotic sensing feedback loops for its continuous updates. Sensing loops can consequently steer measurement, analysis and reconfiguration aimed at more accurate modelling and analysis in DT. The reconfiguration decisions can be autonomous or interactive, keeping human-in-the-loop. The trustworthiness of these decisions can be hindered by inadequate explainability of the rationale, and utility gained in implementing the decision for the given situation among alternatives. Additionally, different decision-making algorithms and models have varying complexity, quality and can result in different utility gained for the model. The inadequacy of explainability can limit the extent to which humans can evaluate the decisions, often leading to updates which are unfit for the given situation, erroneous, compromising the overall accuracy of the model. The novel contribution of this paper is an approach to harnessing explainability in human-in-the-loop DDDAS and DT systems, leveraging bidirectional symbiotic sensing feedback. The approach utilises interpretable machine learning and goal modelling to explainability, and considers trade-off analysis of utility gained. We use examples from smart warehousing to demonstrate the approach.},
langid = {english},
pubstate = {prepublished},
note = {Comment: 11 pages, 1 figure, accepted by the 4th International Conference on InfoSymbiotics/Dynamic Data Driven Applications Systems (DDDAS2022)},
abstract = {The problem attacked in this paper is to obtain the smallest model set which is described by nominal model, parametric uncertainty bound, unstructured uncertainty bound and consistent with a number of noise-free input-output data, under the condition that the denominator of the nominal model is prescribed. For the compatibility with the available robust control theory, the unstructured uncertainty is measured by H∞-norm, while the parametric uncertainty is by parameter variation interval. It is shown that the unstructured uncertainty bound will generally increase if the nominal model error uncertainty is completely regarded as unstructured. Moreover, the identification problem is reduced to a convex optimization problem which is computationally tractable.},
Robust control as a field determines how resilient a control system is to a difference in plant dynamics for a given characteristic. In a real system, there will always be some inaccuracy in the model of plant dynamics, disturbances, or other noise. These unmodeled features will affect plant behavior if they are not anticipated. Robust control gives us tools to design for these perturbations proactively. We can design characteristics such as performance and stability to guarantee as 'robust'.
Robustness is dependent on two features: the characteristic to be guaranteed, and the set of reasonably possible perturbed plants $\mathcal{P}$. Usually the characteristic we're interested in is internal stability or performance. The possible set of plants, however, is less straightforward. The set $\mathcal{P}$ can be structured or unstructured. A structured set in this instance can be a discrete number of possible perturbed plants, or possibly a parametric study with a finite number of parameters. Let's consider an example.
Robustness is dependent on two features: the characteristic to be guaranteed, and the set of reasonably possible perturbed plants $\mathcal{P}$. Usually the characteristic we're interested in is internal stability or performance. The possible set of plants, however, is less straightforward. The set $\mathcal{P}$ can be structured or unstructured. A structured set in this instance can be a discrete number of possible perturbed plants, or possibly a parametric study with a finite number of parameters@doyleFeedbackControlTheory2009. Let's consider an example.
Suppose a plant representing a spring-mass-damper system is described as follows @controltutorialsformatlab&simulinkInvertedPendulumSystem:
Suppose a plant representing a spring-mass-damper system is described as follows @controltutorialsformatlab&simulinkInvertedPendulumSystem:
$$ P = \frac{X(s)}{F(s)} = \frac{1}{ms^2 + bs +k}$$
A structured perturbation might take each of these physical parameters $m$, $b$, and $k$ and attribute a likely range or tolerance to their value:
@ -33,8 +33,15 @@ where $e_m$ is the difference between the nominal mass and the actual as-built m
**Limitation:** *Structured perturbations limit the form of perturbation possible to sample.* Because structured perturbations either are chosen a priori or through a parametric study, the form of possible perturbed plants is limited. Structured perturbations do not allow for unmodelled dynamics to be included as a possible perturbation.
The other type of uncertainty considered is unstructured uncertainty. This type of uncertainty does not assume a form and thus is able to capture unmodelled behavior in its robustness analysis. Unstructured sets are advantageous compared to structured sets for this reason. Robustness with respect to unstructured sets provides a guarantee of resilience to adverse conditions that are unanticipated, or difficult to model.
The other type of uncertainty considered is unstructured uncertainty. This type of uncertainty does not assume a form and thus is able to capture unmodelled behavior in its robustness analysis. Unstructured sets are advantageous compared to structured sets for this reason. Robustness with respect to unstructured sets provides a guarantee of resilience to adverse conditions that are unanticipated, or difficult to model. One popular way of implementing unstructured uncertainty is the disk multiplicative perturbation. The disk multiplicative perturbation is defined as follows:
(The disk multiplicative perturbation)
$$ \tilde P = (1+\Delta W_2) P $$
Where $\Delta$ is a variable stable transfer function with $||\Delta||_\infty <1$,and$W_2$istheuncertaintyprofile.
(Explain how actually getting to W_2 isn't really trivial).
The 'disk' part of the multiplicative disk uncertainty comes from analysis in the complex domain, specifically looking at the Nyquist Stability Criterion. Stability according to this criterion is determined when the loop gain $L$ of a system does not pass through the point -1 during a sweep of all frequencies on the imaginary access. For robust stability, we examine if a system is still stable when calculating the Nyquist plot of $W_2 L$. If it is, then all perturbed plants $\tilde P = (1+\Delta W_2)P$ are also stable.
This is useful for us. If we can find an uncertainty transfer function $W_2$ that we are satisfied with, and pair it with a design of a controller that maintains the Nyquist criterion, then we know our system is robust to any perturbations captured by $||\Delta||_\infty <1$.Robustperformancecanbeachievedusingasimilarprocess@doyleFeedbackControlTheory2009.
$\Delta$ is almost always considered a free variable transfer function. Since $||\Delta||_\infty <1 \text{} \forall \omega$,$\Delta$willnotdecreasetheminimumrobustnessmargin.Thisisfinefordevelopingacontroller,butwhenitcomestoactuallyverifyingrobustnessofacontrollerimplementation,$\Delta$cannotbeavariable.Tocreateaplanttosimulateaperturbedplant,$\Delta$musthaveanexpression.
**Limitation**: *There is no current method for creating random examples of $\Delta$.*
$|W_2(j\omega)|$ is the uncertainty profile. This inequality describes a disk in teh complex plane: at each frequency the point P~/P lies in the disk with center 1, radius |W_2|.
@ -99,3 +99,11 @@ W_2 is basically a transfer function that will always be greater in magnitude th
>>[!important] Robust Performance
>>$$ |||W_1 S | + |W_2 T| ||_\infty <1$$
>>![[Pasted image 20241015172708.png]]
Something really helpful to think about came to mind as a result of watching a Steve Brunton video[^1]. Think about the way that loop gain works:
$$ y = \frac{L}{1+L} r $$
If at a certain frequency $\omega$, L approaches -1, big problems happen. What this means is that the denominator in the above equation gets really small, which means the gain from r to y actually gets really big. If it IS -1, immediate undefined blow up.
This is where robustness comes from. The distance between L and -1 for all frequencies is what robustness is. Less distance, less room for plant perturbation that could make you unstable. More distance, safer response. This gets integrated when you start thinking about $W_2$ and $\Delta$. These two things are how you account for the uncertainty and look at how that gets you closer to -1 or not.
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