From c3309cf4a42b637bef8c8a5044d12065ce27d3c0 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Tue, 3 Mar 2026 15:30:14 -0500 Subject: [PATCH] Auto sync: 2026-03-03 15:30:14 (10 files changed) M 3-research-approach/v3.tex M main.aux M main.blg M main.fdb_latexmk M main.fls M main.log M main.pdf D main.synctex(busy) --- 3-research-approach/v3.tex | 195 +++++------ main.aux | 5 +- main.blg | 6 +- main.fdb_latexmk | 14 +- main.fls | 431 ++++++++++++++++++++++++ main.log | 658 ++++++++++++++++++++++++++++++++++++- main.pdf | Bin 190422 -> 190643 bytes main.synctex(busy) | 0 main.synctex.gz | Bin 245452 -> 245004 bytes main.toc | 4 +- 10 files changed, 1195 insertions(+), 118 deletions(-) delete mode 100644 main.synctex(busy) diff --git a/3-research-approach/v3.tex b/3-research-approach/v3.tex index 5ce05f9..9543fa1 100644 --- a/3-research-approach/v3.tex +++ b/3-research-approach/v3.tex @@ -15,22 +15,40 @@ % ---------------------------------------------------------------------------- % 1. INTRODUCTION AND HYBRID SYSTEMS DEFINITION % ---------------------------------------------------------------------------- +Previous approaches to autonomous control have verified +discrete switching logic or continuous control behavior, but not both +simultaneously. Validation of continuous controllers today consists of +extensive simulation trials. Discrete switching logic for routine operation +has been driven by human operators, whose evaluation includes simulated +control room testing and human factors research. Neither method, despite +being extremely resource intensive, provides rigorous guarantees of control +system behavior. HAHACS bridges this gap by composing formal methods from +computer science with control-theoretic verification, formalizing reactor +operations using the framework of hybrid automata. + +The challenge of hybrid system verification lies in the interaction between +discrete and continuous dynamics. Discrete transitions change the governing +vector field, creating discontinuities in the system's behavior. Traditional +verification techniques designed for purely discrete or purely continuous +systems cannot handle this interaction directly.Our methodology addresses this +challenge through decomposition. We verify discrete switching logic and +continuous mode behavior separately, then compose these guarantees to reason +about the complete hybrid system. This two-layer approach mirrors the structure +of reactor operations themselves: discrete supervisory logic determines which +control mode is active, while continuous controllers govern plant behavior +within each mode. To build a high-assurance hybrid autonomous control system (HAHACS), we must first establish a mathematical description of the system. This work draws on -automata theory, temporal logic, and control theory. The nomenclature across -these fields is far from homogeneous, and the reviewer of this proposal is not -expected to be an expert in all of them simultaneously. To present the research -ideas as clearly as possible, the following definitions are provided. - -A hybrid system is a dynamical system that has both continuous and discrete -states. The specific type of system discussed in this proposal is a continuous -autonomous hybrid system. This means that the system does not have external -input and that continuous states do not change instantaneously when discrete -states change. For our systems of interest, the continuous states are physical -quantities that are always Lipschitz continuous. This nomenclature is borrowed -from the Handbook on Hybrid Systems Control, but is redefined here for -convenience: +automata theory, temporal logic, and control theory. A hybrid system is a +dynamical system that has both continuous and discrete states. The specific type +of system discussed in this proposal is a continuous autonomous hybrid system. +This means that the system does not have external input and that continuous +states do not change instantaneously when discrete states change. For our +systems of interest, the continuous states are physical quantities that are +always Lipschitz continuous. This nomenclature is borrowed from the Handbook on +Hybrid Systems Control \cite{HANDBOOK ON HYBRID SYSTEMS}, but is redefined here +for convenience: \begin{equation} H = (\mathcal{Q}, \mathcal{X}, \mathbf{f}, Init, \mathcal{G}, \delta, \mathcal{R}, Inv) @@ -55,46 +73,16 @@ where: The creation of a HAHACS amounts to the construction of such a tuple together with proof artifacts demonstrating that the intended behavior of the control -system is satisfied by its actual implementation. - -\textcolor{blue}{Previous approaches to autonomous control have verified -discrete switching logic or continuous control behavior, but not both -simultaneously. Validation of continuous controllers today consists of -extensive simulation trials. Discrete switching logic for routine operation -has been driven by human operators, whose evaluation includes simulated -control room testing and human factors research. Neither method, despite -being extremely resource intensive, provides rigorous guarantees of control -system behavior. HAHACS bridges this gap by composing formal methods from -computer science with control-theoretic verification, formalizing reactor -operations using the framework of hybrid automata.} - -\textcolor{blue}{The challenge of hybrid system verification lies in the -interaction between discrete and continuous dynamics. Discrete transitions -change the governing vector field, creating discontinuities in the system's -behavior. Traditional verification techniques designed for purely discrete or -purely continuous systems cannot handle this interaction directly.} - -\textcolor{blue}{Our methodology addresses this challenge through decomposition. We verify -discrete switching logic and continuous mode behavior separately, then compose -these guarantees to reason about the complete hybrid system. This two-layer -approach mirrors the structure of reactor operations themselves: discrete -supervisory logic determines which control mode is active, while continuous -controllers govern plant behavior within each mode.} - -\textcolor{blue}{This approach is tractable now because the infrastructure for each component -has matured. Reactive synthesis from temporal logic specifications has -progressed from theoretical results to practical tools; solvers like Strix -can synthesize controllers from LTL specifications in seconds. Reachability -analysis and barrier certificates for continuous systems have decades of -theoretical foundation and modern computational tools. The novelty is not in +system is satisfied by its actual implementation. This approach is tractable now +because the infrastructure for each component has matured. The novelty is not in the individual pieces, but in the architecture that connects them. By defining -entry, exit, and safety conditions at the discrete level first, we transform -the intractable problem of global hybrid verification into a collection of -local verification problems with clear interfaces. Verification is performed -per mode rather than on the full hybrid system, keeping the analysis tractable -even for complex reactor operations.} +entry, exit, and safety conditions at the discrete level first, we transform the +intractable problem of global hybrid verification into a collection of local +verification problems with clear interfaces. Verification is performed per mode +rather than on the full hybrid system, keeping the analysis tractable even for +complex reactor operations. -\begin{figure}[htbp] +\begin{figure} \centering \begin{tikzpicture}[ state/.style={ @@ -113,9 +101,9 @@ even for complex reactor operations.} ] % States \node[state] (q0) at (0,0) {$q_0$\\Cold\\Shutdown}; - \node[state] (q1) at (4,0) {$q_1$\\Heatup}; - \node[state] (q2) at (8,0) {$q_2$\\Power\\Operation}; - \node[state, fill=red!15] (q3) at (4,-3.5) {$q_3$\\SCRAM}; + \node[state] (q1) at (5,0) {$q_1$\\Heatup}; + \node[state] (q2) at (10,0) {$q_2$\\Power\\Operation}; + \node[state, fill=red!15] (q3) at (5,-3.5) {$q_3$\\SCRAM}; % Normal transitions \draw[trans] (q0) -- node[guard, above] {$T_{avg} > T_{min}$} (q1); @@ -133,9 +121,9 @@ even for complex reactor operations.} % Dynamics labels below states \node[dynamics] at (0,-1.4) {$\dot{x} = f_0(x)$}; - \node[dynamics] at (4,-1.4) {$\dot{x} = f_1(x,u)$}; - \node[dynamics] at (8,-1.4) {$\dot{x} = f_2(x,u)$}; - \node[dynamics] at (4,-4.9) {$\dot{x} = f_3(x)$}; + \node[dynamics] at (6,-1.2) {$\dot{x} = f_1(x,u)$}; + \node[dynamics] at (10,-1.4) {$\dot{x} = f_2(x,u)$}; + \node[dynamics] at (5,-4.9) {$\dot{x} = f_3(x)$}; \end{tikzpicture} \caption{Simplified hybrid automaton for reactor startup. Each discrete state @@ -157,54 +145,6 @@ even for complex reactor operations.} % ---------------------------------------------------------------------------- \subsection{System Requirements and Specifications} - -\textcolor{blue}{Before constructing a HAHACS, we must completely describe its -intended behavior. The behavior of any control system originates in -requirements: statements about what the system must do, must not do, and under -what conditions. For nuclear systems, these requirements derive from multiple -sources including regulatory mandates, design basis analyses, and operating -procedures. The challenge is formalizing these requirements with sufficient -precision that they can serve as the foundation for automated controller -synthesis and verification.} - -Autonomous control systems are fundamentally different from automatic control -systems. The difference lies in the level at which they operate. Automatic -control systems are purely operational systems that maintain setpoints or track -references. Autonomous control systems make decisions about which operational -objectives to pursue. - -\begin{figure}[htbp] - \centering - \begin{tikzpicture}[scale=0.8] - % Pyramid layers - \fill[blue!60!black] (0,4) -- (2,4) -- (1,5.5) -- cycle; - \fill[blue!30!white] (-1.5,2.5) -- (3.5,2.5) -- (2,4) -- (0,4) -- cycle; - \fill[blue!15!white] (-3,1) -- (5,1) -- (3.5,2.5) -- (-1.5,2.5) -- cycle; - - % Labels inside pyramid - \node[font=\small\bfseries, white] at (1,4.5) {Strategic}; - \node[font=\small\bfseries] at (1,3.1) {Operational}; - \node[font=\small\bfseries] at (1,1.6) {Tactical}; - - % Descriptions to the right - \node[anchor=west, font=\small, text width=6cm] at (5.5,4.5) - {\textit{Long-term planning:} maintenance scheduling, capacity planning, economic dispatch}; - \node[anchor=west, font=\small, text width=6cm] at (5.5,3.1) - {\textit{Discrete decisions:} startup/shutdown sequences, power level changes, mode transitions}; - \node[anchor=west, font=\small, text width=6cm] at (5.5,1.6) - {\textit{Continuous control:} temperature regulation, pressure control, load following}; - - % Bracket showing HAHACS scope (simple line with text) - \draw[thick] (-3.3,1) -- (-3.5,1) -- (-3.5,4) -- (-3.3,4); - \node[font=\small, align=center, rotate=90] at (-4.2,2.5) {HAHACS scope}; - \end{tikzpicture} - \caption{Control scope hierarchy in nuclear power operations. Strategic control - (long-term planning) remains with human management. HAHACS addresses the - operational level (discrete mode switching) and tactical level (continuous - control within modes), which together form a hybrid control system.} - \label{fig:strat_op_tact} -\end{figure} - Human control of nuclear power can be divided into three different scopes: strategic, operational, and tactical. Strategic control is high-level and long-term decision making for the plant. This level has objectives that are @@ -233,6 +173,51 @@ the continuous evolution of the plant according to the control input and control law, while the operational level is a discrete state evolution that determines which tactical control law to apply. +%Say something about autonomous control systems near here? + +Before constructing a HAHACS, we must completely describe its +intended behavior. The behavior of any control system originates in +requirements: statements about what the system must do, must not do, and under +what conditions. For nuclear systems, these requirements derive from multiple +sources including regulatory mandates, design basis analyses, and operating +procedures. The challenge is formalizing these requirements with sufficient +precision that they can serve as the foundation for autonomous control system +synthesis and verification. + + +\begin{figure} + \centering + \begin{tikzpicture}[scale=0.8] + % Pyramid layers + \fill[blue!30!white] (0,4) -- (2,4) -- (1,5.) -- cycle; + \fill[blue!20!white] (-1.5,2.5) -- (3.5,2.5) -- (2,4) -- (0,4) -- cycle; + \fill[blue!10!white] (-3,1) -- (5,1) -- (3.5,2.5) -- (-1.5,2.5) -- cycle; + + % Labels inside pyramid + \node[font=\small\bfseries] at (1,4.5) {Strategic}; + \node[font=\small\bfseries] at (1,3.1) {Operational}; + \node[font=\small\bfseries] at (1,1.6) {Tactical}; + + % Descriptions to the right + \node[anchor=west, font=\small, text width=8cm] at (5.5,4.6) + {\textit{Long-term planning:} maintenance scheduling, capacity planning, economic dispatch}; + \node[anchor=west, font=\small, text width=8cm] at (5.5,3.1) + {\textit{Discrete decisions:} startup/shutdown sequences, power level changes, mode transitions}; + \node[anchor=west, font=\small, text width=8cm] at (5.5,1.6) + {\textit{Continuous control:} temperature regulation, pressure control, load following}; + + % Bracket showing HAHACS scope (simple line with text) + \draw[thick] (5.0,1.0) -- (-3.5,1) -- (-3.5,4) -- (2.0,4) -- cycle; + \node[font=\small, align=center, rotate=90] at (-4.2,2.5) {HAHACS scope}; + \end{tikzpicture} + \caption{Control scope hierarchy in nuclear power operations. Strategic control + (long-term planning) remains with human management. HAHACS addresses the + operational level (discrete mode switching) and tactical level (continuous + control within modes), which together form a hybrid control system.} + \label{fig:strat_op_tact} +\end{figure} + + This operational control level is the main reason for the requirement of human operators in nuclear control today. 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Specifications}{8}{}% -\contentsline {subsection}{\numberline {3.2}Discrete Controller Synthesis}{11}{}% +\contentsline {subsection}{\numberline {3.2}Discrete Controller Synthesis}{10}{}% \contentsline {subsection}{\numberline {3.3}Continuous Controllers}{11}{}% \contentsline {subsubsection}{\numberline {3.3.1}Transitory Modes}{12}{}% \contentsline {subsubsection}{\numberline {3.3.2}Stabilizing Modes}{13}{}% \contentsline {subsubsection}{\numberline {3.3.3}Expulsory Modes}{14}{}% -\contentsline {subsection}{\numberline {3.4}Industrial Implementation}{15}{}% +\contentsline {subsection}{\numberline {3.4}Industrial Implementation}{14}{}% \contentsline {section}{\numberline {4}Metrics for Success}{16}{}% \contentsline {paragraph}{TRL 3 \textit {Critical Function and Proof of Concept}}{16}{}% \contentsline {paragraph}{TRL 4 \textit {Laboratory Testing of Integrated Components}}{16}{}%