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Dane Sabo 2025-10-20 17:15:21 -04:00
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\\
Advisor: Dr. Daniel G. Cole\\
dgcole@pitt.edu\\
\\
Track: PhD Mechanical Engineering
}
\date{\today}

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\newpage
% PROJECT SUMMARY
\section*{Project Summary}
@ -99,546 +98,7 @@ 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 mod\documentclass[11pt]{article}
% Page setup
\usepackage[margin=1in]{geometry}
\usepackage{setspace}
\setstretch{1.0}
% Packages
\usepackage{amsmath}
\usepackage{cite}
% Document begins
\begin{document}
% COVER SHEET
\begin{center}
{\Large \textbf{From Cold Start to Critical: Formal Synthesis of Hybrid \\
Controllers for Nuclear Reactor Startup}}
\vspace{0.5in}
\textbf{White Paper}
\vspace{0.25in}
\textbf{NSF Program:} Cyber-Physical Systems (CPS)
\vspace{0.25in}
\textbf{Principal Investigator:} Dane A. Sabo\\
Email: dane.sabo@pitt.edu
\vspace{0.25in}
\textbf{Faculty Advisor:} Dr. Daniel G. Cole\\
Email: dgcole@pitt.edu
\vspace{0.25in}
University of Pittsburgh\\
Department of Mechanical Engineering and Materials Science\\
Swanson School of Engineering
\end{center}
\newpage
% 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. 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}
The goal of this research is to develop a methodology for creating autonomous
hybrid control systems with mathematical guarantees of safe and correct
behavior for nuclear reactor operations. Nuclear reactors are quintessential
hybrid cyber-physical systems where continuous neutron kinetics and
thermal-hydraulics interact with discrete control mode decisions and trip
logic. Hybrid systems combine continuous dynamics with discrete mode
transitions, formally expressed as $\dot{x}(t) = f(x(t),q(t),u(t))$ for
continuous states and $q(k+1) = \nu(x(k),q(k),u(k))$ for discrete
transitions.
If this research is successful, we will be able to do the following:
\begin{enumerate}
\item \textit{Synthesize written procedures into verified control logic.}
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. 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.
\item \textit{Verify continuous control behavior across mode transitions.}
We will develop methods using reachability analysis to ensure continuous
control modes satisfy discrete transition requirements. 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.
\item \textit{Demonstrate autonomous reactor startup control with safety
guarantees.} 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. 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{Limits of Current Practice}
Nuclear reactor control reveals fundamental verification gaps that motivate
formal hybrid control synthesis. These gaps span current operational
practices, human reliability, and even the most advanced formal methods
attempts to date.
Current generation nuclear power plants employ over 3,600 active NRC-licensed
reactor operators who hold legal authority to make critical decisions
including departing from regulations during emergencies. This authority is
both necessary and problematic. The Three Mile Island accident demonstrated
how personnel error led to partial meltdown when operators misread confusing
readings and shut off emergency systems. The President's Commission identified
a fundamental ambiguity: operators hold full responsibility without formal
verification they can fulfill this under all conditions.
Nuclear plant procedures exist in a hierarchy from normal operating procedures
through Emergency Operating Procedures to Severe Accident Management
Guidelines. Despite rigorous development processes including technical
evaluation and simulator validation testing, these procedures fundamentally
lack formal verification. No mathematical proof exists that procedures cover
all possible plant states or that required actions can be completed within
available timeframes. This gap between procedural rigor and mathematical
certainty creates the first major limitation of current practice.
The division between automated and human-controlled functions reveals the
fundamental hybrid control challenge. Highly automated systems handle reactor
protection and emergency core cooling, while human operators retain strategic
decision-making. Current practice treats continuous plant dynamics and
discrete control logic as separate concerns without formal integration. No
application of hybrid control theory exists that could provide mathematical
guarantees across mode transitions.
Human factors compound these verification gaps. Multiple independent analyses
show that 70--80\% of all nuclear power plant events are attributed to human
error rather than equipment failures. More significantly, the IAEA concluded
that human error was the root cause of all severe accidents at nuclear power
plants. The persistence of this ratio despite four decades of improvements
suggests fundamental cognitive limitations rather than remediable
deficiencies.
The Three Mile Island accident provides the definitive case study. When a
pressure-operated relief valve stuck open, instrumentation showed only
commanded position, not actual position. This information gap proved decisive.
When Emergency Core Cooling pumps automatically activated, operators shut them
down based on incorrect assessment. Operators faced over 100 simultaneous
alarms, overwhelming their cognitive capacity. The core suffered 44\% fuel
meltdown before stabilization.
Human Reliability Analysis methods quantify these limitations. Nominal Human
Error Probabilities stand at 0.01 (1\%) for diagnosis tasks under optimal
conditions. These rates degrade dramatically under accident conditions:
inadequate time increases error probability 10-fold, extreme stress by 5-fold,
high complexity by 5-fold. Under combined adverse conditions, human error
probabilities approach 0.1 to 1.0---essentially guaranteed failure.
The underlying causes are fundamental and cannot be overcome through training
alone. Response time limitations constrain effectiveness. Visual perception
requires 100-200 milliseconds, decisions 200-400 milliseconds. Reactor
transients evolve in seconds. Protection systems must respond in milliseconds,
100-1000 times faster than humans. Working memory capacity is limited to
7$\pm$2 chunks, explaining why TMI's 100+ alarms exceeded operators'
processing capacity. These are not training failures---they are fundamental
properties of human cognition.
Recent efforts to apply formal methods to nuclear control show both promise
and remaining gaps. The High Assurance Rigorous Digital Engineering for
Nuclear Safety (HARDENS) project represents the most advanced application to
date. Completed in nine months at a fraction of typical costs, HARDENS
produced a complete Reactor Trip System with full traceability from NRC
requirements through formal specifications to verified binaries.
The project employed impressive formal methods. FRET handled requirements
elicitation. Cryptol provided executable specifications. SAW performed
verification. Automatic code synthesis generated formally verifiable
implementations. This comprehensive approach demonstrated that formal methods
are technically feasible and economically viable for nuclear protection
systems.
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---temperature,
pressure, neutron flux---and discrete control decisions. HARDENS verified the
discrete controller in isolation but not the closed-loop hybrid system
behavior.
Experimental validation presents the second major limitation. HARDENS produced
a demonstrator at Technology Readiness Level 3--4 rather than a
deployment-ready system. The gap between formal verification and actual
deployment involves integration with legacy systems, long-term reliability
under harsh environments, and regulatory acceptance of formal methods as
primary assurance evidence.
These three converging lines reveal the research imperative. Current practice
lacks formal verification of procedures and mode transitions. Human operators
contribute to 70--80\% of incidents despite continuous improvements,
suggesting fundamental rather than remediable limitations. HARDENS
demonstrated feasibility of formal methods but addressed only discrete logic,
leaving hybrid dynamics unverified. The continuous dynamics of reactor physics
combined with discrete control logic demand hybrid automata or differential
dynamic logic that can verify properties spanning both domains. This gap
defines the research opportunity.
\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 that progress from written procedures to verified implementations.
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.
Written procedures in nuclear power are sufficiently detailed that we may
translate them into logical formulae with minimal effort. This translation
forms the foundation of our approach.
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.
Consider a nuclear reactor SCRAM requirement: ``If a high temperature alarm
triggers, control rods must immediately insert and remain inserted until
operator reset.'' This natural language statement translates into temporal
logic as: $G(HighTemp \rightarrow X(RodsInserted \wedge (\neg RodsWithdrawn\
U\ OperatorReset)))$. The specification precisely captures the temporal
relationship between alarm, response, and persistence requirement.
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 state-of-the-art reactive synthesis tools, particularly Strix,
which has demonstrated superior performance in the Reactive Synthesis
Competition through efficient parity game solving algorithms. Strix translates
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. This progression from discrete to continuous design
addresses a key challenge in hybrid system verification.
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 to define continuous
state ranges at discrete transition boundaries and verify that requirements
are satisfied within continuous modes. 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.
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 already developed a 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. The
Advanced Reactor Cyber Analysis and Development Environment (ARCADE) suite
will serve as the integration layer, managing real-time communication between
the Simulink simulation and the Ovation controller. 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 achieving
three intermediate levels. TRL 3 demonstrates that each component works in
isolation. Startup procedures must be translated into temporal logic
specifications that pass realizability analysis. A discrete automaton must be
synthesized with interpretable structure. At least one continuous controller
must be designed with verified transition requirements. This level proves the
fundamental approach on simplified sequences.
TRL 4 demonstrates a complete integrated hybrid controller in simulation. All
startup procedures must be formalized with continuous controllers existing for
all discrete modes. Verification must be complete for all mode transitions.
The integrated controller must execute complete startup sequences with zero
safety violations. This level proves that formal correctness guarantees can be
maintained throughout system integration.
TRL 5 demonstrates the verified controller on industrial control hardware
through hardware-in-the-loop testing. The discrete automaton must be
implemented on Emerson Ovation hardware and verified to match synthesized
specifications exactly. The ARCADE interface must establish stable real-time
communication between Ovation hardware and SmAHTR simulation. Complete
autonomous startup sequences must execute across the full operational
envelope. This level proves that the methodology produces verified controllers
implementable with current technology.
This research succeeds if it achieves TRL 5, establishing both theoretical
validity and practical feasibility. Success provides 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.
By synthesizing provably correct hybrid controllers, we can automate routine
operational sequences that currently require constant human oversight. This
enables a fundamental shift 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.
Small modular reactors represent an ideal deployment target. Nuclear
Regulatory Commission certification requires extensive documentation of
control procedures, operational requirements, and safety analyses written in
structured natural language. These regulatory documents can be translated into
temporal logic specifications using FRET, synthesized into discrete switching
logic using reactive synthesis tools, and verified using reachability analysis
and barrier certificates. The infrastructure of requirements is already
complete as part of licensing. This creates a direct pathway from existing
regulatory documentation to formally verified autonomous controllers.
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---one of the most
regulated and safety-critical domains---this research will establish both
technical feasibility and regulatory pathways for broader adoption across
critical infrastructure.
\newpage
% REFERENCES CITED
\section*{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{princeton}
Princeton University. ``Nuclear Reactor Operator Training.''
\textit{Princeton Plasma Physics Laboratory}, 2023.
\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{IAEA-severe-accidents}
International Atomic Energy Agency. ``Lessons Learned from Severe Nuclear
Accidents.'' IAEA Technical Report, 2016.
\bibitem{Wang2025}
Y. Wang et al. ``Human Error Analysis of 190 Events at Chinese Nuclear
Power Plants from 2007-2020.'' \textit{Nuclear Engineering and Design},
vol. 395, 2025.
\bibitem{Kiniry2022}
J. Kiniry et al. ``High Assurance Rigorous Digital Engineering for Nuclear
Safety (HARDENS).'' NRC Final Technical Report ML22326A307, September 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}
\end{document}e transitions occur safely and as defined by the
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
@ -692,142 +152,71 @@ If this research is successful, we will be able to do the following:
achieve autonomy without retraining costs or developing new equipment.
\end{enumerate}
%
% % IMPACT PARAGRAPH Innovation
% The innovation is unifying discrete synthesis and continuous verification to
% enable end-to-end correctness guarantees for hybrid systems.
% % Outcome Impact
% If successful, control engineers will be able to create autonomous controllers from existing
% procedures with mathematical proof of correct behavior, making high-assurance
% autonomous control practical for safety-critical applications.
% % Impact/Pay-off
% This capability is essential for economic viability of next-generation nuclear
% power. Small modular reactors represent a promising solution to growing energy
% demands, but success depends on reducing per-megawatt operating costs through
% increased autonomy. This research will provide the tools to achieve that autonomy
% while maintaining the exceptional safety record required by the nuclear industry.
\section{State of the Art and Limits of Current Practice}
\section{Limits of Current Practice}
Current generation nuclear power plants employ over 3,600 active NRC-licensed
reactor operators who hold legal authority to make critical decisions
including departing from regulations during emergencies. This authority is
both necessary and problematic, and has caused major nuclear accidents such as
the Three Mile Island Accident. The Three Mile Island accident demonstrated
how personnel error led to partial meltdown when operators misread confusing
readings and shut off emergency systems. The President's Commission identified
a fundamental ambiguity: operators hold full responsibility without formal
verification they can fulfill this under all conditions.
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.
Nuclear plant procedures exist in a hierarchy from normal operating procedures
through Emergency Operating Procedures to Severe Accident Management
Guidelines. Despite rigorous development processes including technical
evaluation and simulator validation testing, these procedures fundamentally
lack formal verification. No mathematical proof exists that procedures cover
all possible plant states or that required actions can be completed within
available timeframes.
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.
% The division between automated and human-controlled functions reveals the
% fundamental hybrid control challenge. Highly automated systems handle reactor
% protection and emergency core cooling, while human operators retain strategic
% decision-making. Current practice treats continuous plant dynamics and
% discrete control logic as separate concerns without formal integration. No
% application of hybrid control theory exists that could provide mathematical
% guarantees across mode transitions.
%
Human factors compound these verification gaps. 70--80\% of all nuclear power
plant events are attributed to human error rather than equipment failures. More
significantly, the IAEA concluded that human error was the root cause of all
severe accidents at nuclear power plants. The persistence of this ratio despite
four decades of improvements suggests fundamental cognitive limitations rather
than remediable deficiencies.
The Three Mile Island accident provides the definitive case study. When a
pressure-operated relief valve stuck open, instrumentation showed only
commanded position, not actual position. This information gap proved decisive.
When Emergency Core Cooling pumps automatically activated, operators shut them
down based on incorrect assessment. Operators faced over 100 simultaneous
alarms, overwhelming their cognitive capacity. The core suffered 44\% fuel
meltdown before stabilization.
Human Reliability Analysis methods quantify these limitations. Nominal Human
Error Probabilities stand at 0.01 (1\%) for diagnosis tasks under optimal
conditions. These rates degrade dramatically under accident conditions:
inadequate time increases error probability 10-fold, extreme stress by 5-fold,
high complexity by 5-fold. Under combined adverse conditions, human error
probabilities approach 0.1 to 1.0---essentially guaranteed failure.
The underlying causes are fundamental and cannot be overcome through training
alone. Response time limitations constrain effectiveness. Visual perception
requires 100-200 milliseconds, decisions 200-400 milliseconds. Reactor
transients evolve in seconds. Protection systems must respond in milliseconds,
100-1000 times faster than humans. Working memory capacity is limited to
7$\pm$2 chunks, explaining why TMI's 100+ alarms exceeded operators'
processing capacity. These are not training failures---they are fundamental
properties of human cognition.
Recent efforts to apply formal methods to nuclear control show both promise
and remaining gaps. The High Assurance Rigorous Digital Engineering for
Nuclear Safety (HARDENS) project represents the most advanced application to
date. Completed in nine months at a fraction of typical costs, HARDENS
produced a complete Reactor Trip System with full traceability from NRC
requirements through formal specifications to verified binaries.
The project employed impressive formal methods. FRET handled requirements
elicitation. Cryptol provided executable specifications. SAW performed
verification. Automatic code synthesis generated formally verifiable
implementations. This comprehensive approach demonstrated that formal methods
are technically feasible and economically viable for nuclear protection
systems.
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---temperature,
pressure, neutron flux---and discrete control decisions. HARDENS verified the
discrete controller in isolation but not the closed-loop hybrid system
behavior.
Experimental validation presents the second major limitation. HARDENS produced
a demonstrator at Technology Readiness Level 3--4 rather than a
deployment-ready system. The gap between formal verification and actual
deployment involves integration with legacy systems, long-term reliability
under harsh environments, and regulatory acceptance of formal methods as
primary assurance evidence.
These three converging lines reveal the research imperative. Current practice
lacks formal verification of procedures and mode transitions. Human operators
contribute to 70--80\% of incidents despite continuous improvements,
suggesting fundamental rather than remediable limitations. HARDENS
demonstrated feasibility of formal methods but addressed only discrete logic,
leaving hybrid dynamics unverified. The continuous dynamics of reactor physics
combined with discrete control logic demand hybrid automata or differential
dynamic logic that can verify properties spanning both domains. This gap
defines the research opportunity.
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 that progress from written procedures to verified implementations.
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.
Written procedures in nuclear power are sufficiently detailed that we may
translate them into logical formulae with minimal effort. This 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$). These
operators enable precise specification of time-dependent requirements.
These specifications precisely define behavior in a way that natural language is
not able to reproduce. The most efficient path to accomplish this translation is
through NASA's Formal Requirements Elicitation Tool (FRET). FRET employs
FRETish, a specialized requirements language that restricts requirements to
easily understood components while eliminating ambiguity. FRET enforces
structure by requiring all requirements to contain six components: Scope,
Condition, Component, Shall, Timing, and Response.
performed by human operators are highly prescriptive and well-documented. To
formalize these procedures, we will use temporal logic, which captures system
behaviors through temporal relations. Linear Temporal Logic provides four
fundamental operators: next ($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
@ -847,32 +236,28 @@ 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 state-of-the-art reactive synthesis tools, particularly Strix,
which has demonstrated superior performance in the Reactive Synthesis
Competition through efficient parity game solving algorithms. Strix translates
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
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.
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. This progression from discrete to continuous design
addresses a key challenge in hybrid system verification.
continuous controllers.
The discrete automaton transitions mark decision points for switching between
continuous control modes and define their strategic objectives. We will
@ -897,14 +282,14 @@ 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 to define continuous
state ranges at discrete transition boundaries and verify that requirements
are satisfied within continuous modes. Assume-guarantee contracts will be
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.
Barrier certificates will prove that mode transitions are satisfied. Control
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.
@ -917,60 +302,38 @@ 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.
capacity. We have access to an already developed high-fidelity SmAHTR model in Simulink that
captures the thermal-hydraulic and neutron kinetics behavior.
We have already developed a 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. The
Advanced Reactor Cyber Analysis and Development Environment (ARCADE) suite
will serve as the integration layer, managing real-time communication between
the Simulink simulation and the Ovation controller. This hardware-in-the-loop
configuration enables validation of the controller implementation on actual
industrial control equipment.
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.
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.
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 achieving
three intermediate levels. TRL 3 demonstrates that each component works in
isolation. Startup procedures must be translated into temporal logic
specifications that pass realizability analysis. A discrete automaton must be
synthesized with interpretable structure. At least one continuous controller
must be designed with verified transition requirements. This level proves the
fundamental approach on simplified sequences.
TRL 4 demonstrates a complete integrated hybrid controller in simulation. All
startup procedures must be formalized with continuous controllers existing for
all discrete modes. Verification must be complete for all mode transitions.
The integrated controller must execute complete startup sequences with zero
safety violations. This level proves that formal correctness guarantees can be
maintained throughout system integration.
TRL 5 demonstrates the verified controller on industrial control hardware
through hardware-in-the-loop testing. The discrete automaton must be
implemented on Emerson Ovation hardware and verified to match synthesized
specifications exactly. The ARCADE interface must establish stable real-time
communication between Ovation hardware and SmAHTR simulation. Complete
autonomous startup sequences must execute across the full operational
envelope. This level proves that the methodology produces verified controllers
implementable with current technology.
This research succeeds if it achieves TRL 5, establishing both theoretical
validity and practical feasibility. Success provides a clear pathway for
nuclear industry adoption and broader application to safety-critical
autonomous systems.
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}
@ -984,19 +347,17 @@ 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.
By synthesizing provably correct hybrid controllers, we can automate routine
operational sequences that currently require constant human oversight. This
enables a fundamental shift 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.
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
@ -1007,27 +368,16 @@ 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.
Small modular reactors represent an ideal deployment target. Nuclear
Regulatory Commission certification requires extensive documentation of
control procedures, operational requirements, and safety analyses written in
structured natural language. These regulatory documents can be translated into
temporal logic specifications using FRET, synthesized into discrete switching
logic using reactive synthesis tools, and verified using reachability analysis
and barrier certificates. The infrastructure of requirements is already
complete as part of licensing. This creates a direct pathway from existing
regulatory documentation to formally verified autonomous controllers.
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---one of the most
regulated and safety-critical domains---this research will establish both
technical feasibility and regulatory pathways for broader adoption across
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
@ -1040,10 +390,6 @@ critical infrastructure.
U.S. Nuclear Regulatory Commission. ``10 CFR Part 55 - Operators' Licenses.''
\textit{Code of Federal Regulations}, 2024.
\bibitem{princeton}
Princeton University. ``Nuclear Reactor Operator Training.''
\textit{Princeton Plasma Physics Laboratory}, 2023.
\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.
@ -1060,18 +406,9 @@ DOE-HDBK-1028-2009, June 2009.
World Nuclear Association. ``Safety of Nuclear Power Reactors.''
\textit{World Nuclear Association Information Library}, 2020.
\bibitem{IAEA-severe-accidents}
International Atomic Energy Agency. ``Lessons Learned from Severe Nuclear
Accidents.'' IAEA Technical Report, 2016.
\bibitem{Wang2025}
Y. Wang et al. ``Human Error Analysis of 190 Events at Chinese Nuclear
Power Plants from 2007-2020.'' \textit{Nuclear Engineering and Design},
vol. 395, 2025.
\bibitem{Kiniry2022}
J. Kiniry et al. ``High Assurance Rigorous Digital Engineering for Nuclear
Safety (HARDENS).'' NRC Final Technical Report ML22326A307, September 2022.
Safety (HARDENS).'' NRC Final Technical Report ML22326A307, October 2022.
\bibitem{eia_lcoe_2022}
U.S. Energy Information Administration. ``Levelized Costs of New Generation
@ -1083,4 +420,3 @@ Upending Power Grids and Threatening the Climate.'' Web article, 2024.
\end{thebibliography}
\end{document}