% PROJECT SUMMARY
\section*{Project Summary}

\subsection*{Overview}

This research will develop a methodology for creating autonomous hybrid control
systems with mathematical guarantees of safe and correct behavior. Nuclear power
plants require the highest levels of control system reliability, where failures
can result in significant economic losses or radiological release. Currently,
nuclear operations rely on extensively trained human operators who follow
detailed written procedures to manage reactor control. However, reliance on
human operators prevents introduction of autonomous control capabilities and
creates fundamental economic challenges for next-generation reactor designs.
Without introducing automation, emerging technologies like small modular
reactors face significantly higher per-megawatt staffing costs than conventional
plants, threatening their economic viability.

To address this need, we will combine formal methods from computer science 
with control theory to build hybrid control systems that are correct by 
construction. Hybrid systems use discrete logic to switch between continuous 
control modes, similar to how operators change control strategies. Existing 
formal methods can generate provably correct switching logic from written 
requirements, but they cannot handle the continuous dynamics that occur during 
transitions between modes. Meanwhile, traditional control theory can verify 
continuous behavior but lacks tools for proving correctness of discrete 
switching decisions. By synthesizing discrete mode transitions directly from 
written operating procedures and verifying continuous behavior between 
transitions, we can create hybrid control systems with end-to-end correctness 
guarantees.

\subsection*{Intellectual Merit}

The intellectual merit lies in unifying discrete synthesis and continuous 
verification to enable end-to-end correctness guarantees for hybrid systems. 
This research will advance knowledge by developing a systematic, 
tool-supported methodology for translating written procedures into temporal 
logic, synthesizing provably correct discrete switching logic, and developing 
verified continuous controllers. The approach addresses a fundamental gap in 
hybrid system design by bridging formal methods from computer science and 
control theory.

\subsection*{Broader Impacts}

This research directly addresses the multi-billion dollar operations and 
maintenance cost challenge facing nuclear power deployment. By synthesizing 
provably correct hybrid controllers, we can automate routine operational 
sequences that currently require constant human oversight, enabling a shift 
from direct operator control to supervisory monitoring. Beyond nuclear 
applications, this research will establish a generalizable framework for 
autonomous control of safety-critical systems including chemical process 
control, aerospace systems, and autonomous transportation.

\newpage

% RESEARCH DESCRIPTION
\section*{Research Description}

\section{Objectives}
% GOAL PARAGRAPH
The goal of this research is to develop a methodology for creating autonomous
control systems with event-driven control laws that have guarantees of safe and
correct behavior.

% INTRODUCTORY PARAGRAPH Hook
Nuclear power relies on extensively trained operators who follow detailed
written procedures to manage reactor control. Based on these procedures and
operators' interpretation of plant conditions, operators make critical decisions
about when to switch between control objectives. 
% Gap
While human operators have maintained the nuclear industry's exceptional safety
record, reliance on human operators has created an economic challenge for
next-generation nuclear power plants. Small modular reactors face significantly
higher per-megawatt staffing costs than conventional plants, threatening their
economic viability. Autonomous control systems are needed that can safely manage
complex operational sequences with the same assurance as human-operated systems,
but without constant supervision.

% APPROACH PARAGRAPH Solution
To address this need, we will combine formal methods from computer science with
control theory to build hybrid control systems that are correct by construction. 
% Rationale
Hybrid systems use discrete logic to switch between continuous control modes,
similar to how operators change control strategies. Existing formal methods
generate provably correct switching logic but cannot handle continuous dynamics
during transitions, while traditional control theory verifies continuous
behavior but lacks tools for proving discrete switching correctness. 
% Hypothesis and Technical Approach
We will bridge this gap through a three-stage methodology. First, we will
translate written operating procedures into temporal logic specifications using
NASA's Formal Requirements Elicitation Tool (FRET), which structures
requirements into scope, condition, component, timing, and response elements.
This structured approach enables realizability checking to identify conflicts
and ambiguities in procedures before implementation. Second, we will synthesize
discrete mode switching logic from these specifications using reactive synthesis
tools such as Strix, which generates deterministic automata that are provably
correct by construction. Third, we will develop and verify continuous
controllers for each discrete mode using standard control theory and
reachability analysis. We will classify continuous modes based on their
transition objectives, and then employ assume-guarantee contracts and barrier
certificates to prove that mode transitions occur safely and as defined by the
deterministic automata. This compositional approach enables local verification
of continuous modes without requiring global trajectory analysis across the
entire hybrid system. We will demonstrate this methodology by developing an
autonomous startup controller for a Small Modular Advanced High Temperature
Reactor (SmAHTR) and implementing it on an Emerson Ovation control system using
the ARCADE hardware-in-the-loop platform. 
% Pay-off
This approach will demonstrate autonomous control can be used for complex
nuclear power operations while maintaining safety guarantees.

\vspace{11pt}

% OUTCOMES PARAGRAPHS
If this research is successful, we will be able to do the following:
\begin{enumerate}
  % OUTCOME 1 Title
  \item \textit{Synthesize written procedures into verified control logic.} 
    % Strategy
    We will develop a methodology for converting written operating procedures
    into formal specifications. These specifications will be synthesized into
    discrete control logic using reactive synthesis tools. This process uses
    structured intermediate representations to bridge natural language and
    mathematical logic. 
    % Outcome
    Control engineers will be able to generate mode-switching controllers from
    regulatory procedures with little formal methods expertise, reducing
    barriers to high-assurance control systems.

    % OUTCOME 2 Title
  \item \textit{Verify continuous control behavior across mode transitions. }
    % Strategy
    We will develop methods using reachability analysis to ensure continuous control modes 
    satisfy discrete transition requirements. 
    % Outcome
    Engineers will be able to design continuous controllers using standard
    practices while ensuring system correctness and proving mode transitions
    occur safely at the right times.

    % OUTCOME 3  Title
  \item \textit{Demonstrate autonomous reactor startup control with safety
    guarantees. }
    % Strategy
    We will implement this methodology on a small modular reactor simulation
    using industry-standard control hardware. This trial will include multiple
    coordinated control modes from cold shutdown through criticality to power
    operation on a SmAHTR reactor simulation in a hardware-in-the-loop
    experiment. 
    % Outcome
    Control engineers will be able to implement high-assurance autonomous
    controls on industrial platforms they already use, enabling users to
    achieve autonomy without retraining costs or developing new equipment.

\end{enumerate}
\section{State of the Art and Limits of Current Practice}

Automation of some nuclear power operations is already performed today. Highly
automated systems handle reactor protection and emergency core cooling, while
human operators retain strategic decision-making. Autonomous systems are trusted
to handle emergency situations that are considered terminal operations, but
otherwise introduce too much risk to reactor operations. Contrary to this notion
is the fact that 70--80\% of all nuclear power plant events are attributed to
human error rather than equipment failures. The persistence of this ratio despite
four decades of improvements to procedures and control rooms suggests
fundamental cognitive limitations rather than remediable deficiencies.

The Nuclear Regulatory Commission has recognized that introducing automation
into the control room is the only way forward. Recent efforts to apply formal
methods to nuclear control have shown both promise and remaining gaps. The High
Assurance Rigorous Digital Engineering for Nuclear Safety (HARDENS) project
represents the most advanced application to date. HARDENS produced a complete
Reactor Trip System with full traceability from NRC requirements through formal
specifications to verified binaries of a controller implementation. The project
employed formal methods along the control design stack. This comprehensive
approach demonstrated that formal methods may be technically feasible and
economically viable for nuclear protection systems.

But despite these accomplishments, HARDENS has a fundamental limitation directly
relevant to our work. The project addressed only discrete digital control logic
without modeling or verifying continuous reactor dynamics. Real reactor safety
depends on interaction between continuous processes and discrete control
decisions. HARDENS verified the discrete controller in isolation but not the
closed-loop hybrid system behavior. 

\section{Research Approach}

This research will overcome the identified limitations by combining formal 
methods from computer science with control theory to build hybrid control 
systems that are correct by construction. We accomplish this through three 
main thrusts:

\begin{enumerate} 

  \item We will translate natural language procedures and
  requirements into temporal logic specifications using the Formal Requirements
  Elicitation Tool (FRET). 

  \item We will synthesize these temporal logic
  specifications into the discrete component of the hybrid controller using
  reactive synthesis. 

  \item We will build continuous control modes that satisfy discrete controller
  transition requirements.

\end{enumerate}

Commercial nuclear power operations remain manually controlled despite
significant advances in control systems. The key insight is that procedures
performed by human operators are highly prescriptive and well-documented. To
formalize these procedures, we will use temporal logic, which captures system
behaviors through temporal relations. Linear Temporal Logic provides four
fundamental operators: next ($X$), eventually ($F$), globally ($G$), and until
($U$). These operators enable precise specification of time-dependent
requirements. The most efficient path to accomplish this translation is through
NASA's Formal Requirements Elicitation Tool (FRET). FRET employs FRETish, a
specialized requirements language that restricts requirements to easily
understood components while eliminating ambiguity. FRET enforces structure by
requiring all requirements to contain six components: Scope, Condition,
Component, Shall, Timing, and Response.

FRET provides functionality to check realizability of a system. Realizability 
analysis determines whether written requirements are complete by examining the 
six structural components. Complete requirements neither conflict with one 
another nor leave any behavior undefined. Systems that are not realizable 
contain behavioral inconsistencies that represent the physical equivalent of 
software bugs. Using FRET during autonomous controller development allows us 
to identify and resolve these errors systematically. FRET exports requirements 
in temporal logic format compatible with reactive synthesis tools, enabling 
the second thrust of our approach.

Reactive synthesis is an active research field focused on generating discrete 
controllers from temporal logic specifications. The term reactive indicates 
that the system responds to environmental inputs to produce control outputs. 
These synthesized systems are finite in size, where each node represents a 
unique discrete state. The connections between nodes, called state 
transitions, specify the conditions under which the discrete controller moves 
from state to state. This complete mapping constitutes a discrete automaton.

We will employ reactive synthesis tools which translate linear temporal logic
specifications into deterministic automata automatically while maximizing
generated automata quality. Once constructed, the automaton can be
straightforwardly implemented using standard programming control flow
constructs. The discrete automata representation yields an important theoretical 
guarantee. Because the discrete automaton is synthesized entirely through 
automated tools from design requirements and operating procedures, we can 
prove that the automaton---and therefore our hybrid switching behavior---is 
correct by construction. 

This correctness guarantee is paramount. Mode switching represents the primary
responsibility of human operators in control rooms today. Human operators
possess the advantage of real-time judgment. When mistakes occur, they can
correct them dynamically. Autonomous control lacks this adaptive advantage. By
synthesizing controllers from logical specifications with guaranteed
correctness, we eliminate the possibility of switching errors.

While discrete system components will be synthesized with correctness 
guarantees, they represent only half of the complete system. The continuous 
modes will be developed after discrete automaton construction, leveraging the 
automaton structure and transitions to design multiple smaller, specialized 
continuous controllers. 

The discrete automaton transitions mark decision points for switching between 
continuous control modes and define their strategic objectives. We will 
classify three types of high-level continuous controller objectives: 
Stabilizing modes maintain the hybrid system within its current discrete mode, 
corresponding to steady-state normal operating modes like full-power 
load-following control. Transitory modes have the primary goal of 
transitioning the hybrid system from one discrete state to another, such as 
controlled warm-up procedures. Expulsory modes are specialized transitory 
modes with additional safety constraints that ensure the system is directed to 
a safe stabilizing mode during failure conditions, such as reactor SCRAM.

Building continuous modes after constructing discrete automata enables local 
controller design focused on satisfying discrete transitions. The primary 
challenge in hybrid system verification is ensuring global stability across 
transitions. Current techniques struggle with this problem because dynamic 
discontinuities complicate verification. This work alleviates these problems 
by designing continuous controllers specifically with transitions in mind. By 
decomposing continuous modes according to their required behavior at 
transition points, we avoid solving trajectories through the entire hybrid 
system.

To ensure continuous modes satisfy their requirements, we will employ three 
complementary techniques. Reachability analysis computes the reachable set of 
states for a given input set. We will use reachability when continuous 
state ranges at discrete transition boundaries are defined and verify that 
continuous modes only can reach such defined ranges. Otherwise, assume-guarantee contracts will be 
employed when continuous state boundaries are not explicitly defined. For any 
given mode, the input range for reachability analysis is defined by the output 
ranges of discrete modes that transition to it. This compositional approach 
ensures each continuous controller is prepared for its possible input range. 
Finally, barrier certificates will prove that mode transitions are satisfied. Control 
barrier functions provide a method to certify safety by establishing 
differential inequality conditions that guarantee forward invariance of safe 
sets.

Combining these three techniques will enable us to prove that continuous 
components satisfy discrete requirements and thus complete system behavior. To 
demonstrate this methodology, we will develop an autonomous startup controller 
for a Small Modular Advanced High Temperature Reactor (SmAHTR). SmAHTR 
represents an ideal test case with well-documented startup procedures that 
must transition through multiple distinct operational modes: initial cold 
conditions, controlled heating to operating temperature, approach to 
criticality, low-power physics testing, and power ascension to full operating 
capacity. We have access to an already developed high-fidelity SmAHTR model in Simulink that 
captures the thermal-hydraulic and neutron kinetics behavior. 

The synthesized hybrid controller will be implemented on an Emerson Ovation
control system platform, which is representative of industry-standard control
hardware. This control system will be used in a hardware-in-the-loop simulation,
where the Advanced Reactor Cyber Analysis and Development Environment
(ARCADE) suite will serve as the integration layer. This
hardware-in-the-loop configuration enables validation of the controller
implementation on actual industrial control equipment.

\section{Metrics of Success}

This research will be measured by advancement through Technology Readiness
Levels, progressing from fundamental concepts to validated prototype
demonstration. The work begins at TRL 2--3 and aims to reach TRL 5, where system
components operate successfully in a relevant laboratory environment. TRLs
provide the ideal success metric because they explicitly measure the gap between
academic proof-of-concept and practical deployment. This gap is precisely what
our work aims to bridge. TRLs capture both theoretical rigor and practical
feasibility simultaneously. The nuclear industry already uses TRLs for
technology assessment, making this metric directly relevant to potential
adopters.

Moving from current state (TRL 2--3) to target (TRL 5) requires progressing
through component isolation, system integration, and hardware validation. By
reaching TRL 5, we will have demonstrated a complete autonomous hybrid
controller operating on industrial control hardware through hardware-in-the-loop
testing. Achieving TRL 5 establishes both theoretical validity and practical
feasibility, proving that the methodology produces verified controllers
implementable with current technology and providing a clear pathway for nuclear
industry adoption and broader application to safety-critical autonomous systems.

\section{Broader Impacts}

Nuclear power presents both a compelling application domain and an urgent 
economic challenge. Recent interest in powering artificial intelligence 
infrastructure has renewed focus on small modular reactors for hyperscale 
datacenters. According to the U.S. Energy Information Administration, advanced 
nuclear power entering service in 2027 is projected to cost \$88.24 per 
megawatt-hour. With datacenter electricity demand projected to reach 1,050 
terawatt-hours annually by 2030, operations and maintenance costs represent 
approximately 23--30\% of total levelized cost, translating to \$21--28 
billion annually for projected datacenter demand.

This research directly addresses the multi-billion dollar O\&M cost challenge.
Current nuclear operations require full control room staffing for each reactor.
These staffing requirements drive high O\&M costs, particularly for smaller
reactor designs where the same overhead must be spread across lower power
output. The economic burden threatens the viability of next-generation nuclear
technologies. But, by synthesizing provably correct hybrid controllers, we can
automate routine operational sequences that currently require constant human
oversight. This enables a change from direct operator control to
supervisory monitoring where operators oversee multiple autonomous reactors
rather than manually controlling individual units. The transition fundamentally
changes the economics of nuclear operations.

The correct-by-construction methodology is critical for this transition. 
Traditional automation approaches cannot provide sufficient safety guarantees 
for nuclear applications where regulatory requirements and public safety 
concerns demand the highest levels of assurance. By formally verifying both 
discrete mode-switching logic and continuous control behavior, this research 
will produce controllers with mathematical proofs of correctness. These 
guarantees enable automation to safely handle routine operations that 
currently require human operators to follow written procedures.

Beyond nuclear applications, this research will establish a generalizable
framework for autonomous control of safety-critical systems. The methodology of
translating operational procedures into formal specifications, synthesizing
discrete switching logic, and verifying continuous mode behavior applies to any
hybrid system with documented operational requirements. Potential applications
include chemical process control, aerospace systems, and autonomous
transportation. These domains share similar economic and safety considerations
that favor increased autonomy with provable correctness guarantees. By
demonstrating this approach in nuclear power this research will establish both
technical feasibility and regulatory pathways for broader adoption across
critical infrastructure.

\newpage

% REFERENCES CITED

\begin{thebibliography}{99}

\bibitem{10CFR55}
U.S. Nuclear Regulatory Commission. ``10 CFR Part 55 - Operators' Licenses.''
\textit{Code of Federal Regulations}, 2024.

\bibitem{Kemeny1979}
J. G. Kemeny et al. ``Report of the President's Commission on the Accident
at Three Mile Island.'' U.S. Government Printing Office, October 1979.

\bibitem{NUREG-0899}
U.S. Nuclear Regulatory Commission. ``Guidelines for the Preparation of
Emergency Operating Procedures.'' NUREG-0899, August 1982.

\bibitem{DOE-HDBK-1028-2009}
U.S. Department of Energy. ``Human Performance Improvement Handbook.''
DOE-HDBK-1028-2009, June 2009.

\bibitem{WNA2020}
World Nuclear Association. ``Safety of Nuclear Power Reactors.''
\textit{World Nuclear Association Information Library}, 2020.

\bibitem{Kiniry2022}
J. Kiniry et al. ``High Assurance Rigorous Digital Engineering for Nuclear
Safety (HARDENS).'' NRC Final Technical Report ML22326A307, October 2022.

\bibitem{eia_lcoe_2022}
U.S. Energy Information Administration. ``Levelized Costs of New Generation
Resources in the Annual Energy Outlook 2022.'' Report, March 2022.

\bibitem{eesi_datacenter_2024}
Environmental and Energy Study Institute. ``Data Center Energy Needs are
Upending Power Grids and Threatening the Climate.'' Web article, 2024.

\end{thebibliography}