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2-state-of-the-art/v2.tex
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@ -15,7 +15,7 @@ Emergency Operating Procedures (EOPs) for design-basis accidents, Severe
Accident Management Guidelines (SAMGs) for beyond-design-basis events, and Accident Management Guidelines (SAMGs) for beyond-design-basis events, and
Extensive Damage Mitigation Guidelines (EDMGs) for catastrophic damage Extensive Damage Mitigation Guidelines (EDMGs) for catastrophic damage
scenarios. These procedures must comply with 10 CFR 50.34(b)(6)(ii) and are scenarios. These procedures must comply with 10 CFR 50.34(b)(6)(ii) and are
developed using guidance from NUREG-0900~\cite{NUREG-0899, 10CFR50.34}, but their developed using guidance from NUREG-0899~\cite{NUREG-0899, 10CFR50.34}, but their
development relies fundamentally on expert judgment and simulator validation development relies fundamentally on expert judgment and simulator validation
rather than formal verification. Procedures undergo technical evaluation, rather than formal verification. Procedures undergo technical evaluation,
simulator validation testing, and biennial review as part of operator simulator validation testing, and biennial review as part of operator

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@ -452,11 +452,11 @@ reachable within time horizon $T$:
\text{Reach}(\mathcal{X}_{entry}, f_i, [0,T]) \cap \mathcal{X}_{exit} \neq \emptyset \text{Reach}(\mathcal{X}_{entry}, f_i, [0,T]) \cap \mathcal{X}_{exit} \neq \emptyset
\] \]
Because the discrete controller defines clear boundaries in continuous state \textcolor{blue}{Because the discrete controller defines clear boundaries in continuous state
space, the verification problem for each transitory mode is well-posed. We know space, the verification problem for each transitory mode is well-posed. We know
the possible initial conditions, we know the target conditions, and we know the the possible initial conditions, we know the target conditions, and we know the
safety envelope. The verification task is to confirm that the candidate safety envelope. The verification task is to confirm that the candidate
continuous controller achieves the objective from all possible starting points. continuous controller achieves the objective from all possible starting points.}
Several tools exist for computing reachable sets of hybrid Several tools exist for computing reachable sets of hybrid
systems, including CORA, Flow*, SpaceEx, and JuliaReach. The choice of tool systems, including CORA, Flow*, SpaceEx, and JuliaReach. The choice of tool
@ -478,20 +478,18 @@ appropriate to the fidelity of the reactor models available.
\subsubsection{Stabilizing Modes} \subsubsection{Stabilizing Modes}
\textcolor{blue}{Stabilizing modes are continuous controllers with an objective Stabilizing modes are continuous controllers with an objective of maintaining a
of maintaining a particular discrete state indefinitely. Rather than driving particular discrete state indefinitely. Rather than driving the system toward an
the system toward an exit condition, they keep the system within a safe exit condition, they keep the system within a safe operating region. Examples
operating region. Examples include steady-state power operation, hot standby, include steady-state power operation, hot standby, and load-following at
and load-following at constant power level.} constant power level. Reachability analysis for stabilizing modes may not be a
suitable approach to validation. Instead, we plan to use barrier certificates.
Barrier certificates analyze the dynamics of the system to determine whether
flux across a given boundary exists. They evaluate whether any trajectory leaves
a given boundary. This definition is exactly what defines the validity of a
stabilizing continuous control mode.
Reachability analysis for stabilizing modes may not be the most prudent approach A barrier certificate (or control barrier function) is a
to validation. Instead, barrier certificates must be used. Barrier certificates
analyze the dynamics of the system to determine whether flux across a given
boundary exists. They evaluate whether any trajectory leaves a given boundary.
This definition is exactly what defines the validity of a stabilizing continuous
control mode.
\textcolor{blue}{A barrier certificate (or control barrier function) is a
scalar function $B: \mathcal{X} \rightarrow \mathbb{R}$ that certifies forward scalar function $B: \mathcal{X} \rightarrow \mathbb{R}$ that certifies forward
invariance of a safe set. The idea is analogous to Lyapunov functions for invariance of a safe set. The idea is analogous to Lyapunov functions for
stability: rather than computing trajectories explicitly, we find a certificate stability: rather than computing trajectories explicitly, we find a certificate
@ -504,7 +502,7 @@ barrier certificate condition requires:
This condition states that on the boundary of the safe set (where $B(x) = 0$), This condition states that on the boundary of the safe set (where $B(x) = 0$),
the time derivative of $B$ is non-negative. Geometrically, this means the the time derivative of $B$ is non-negative. Geometrically, this means the
vector field points inward or tangent to the boundary, never outward. If this vector field points inward or tangent to the boundary, never outward. If this
condition holds, no trajectory starting inside $\mathcal{C}$ can ever leave.} condition holds, no trajectory starting inside $\mathcal{C}$ can ever leave.
Because the design of the discrete controller defines careful boundaries in Because the design of the discrete controller defines careful boundaries in
continuous state space, the barrier is known prior to designing the continuous continuous state space, the barrier is known prior to designing the continuous
@ -513,13 +511,17 @@ complication in validating stabilizing continuous control modes. The discrete
specifications tell us what region must be invariant; the barrier certificate specifications tell us what region must be invariant; the barrier certificate
confirms that the candidate controller achieves this invariance. confirms that the candidate controller achieves this invariance.
\textcolor{blue}{Finding barrier certificates can be formulated as a Finding barrier certificates can be formulated as a
sum-of-squares (SOS) optimization problem for polynomial systems, or solved sum-of-squares (SOS) optimization problem for polynomial systems, or solved
using satisfiability modulo theories (SMT) solvers for broader classes of using satisfiability modulo theories (SMT) solvers for broader classes of
dynamics. The key advantage is that the verification is independent of how dynamics. The key advantage is that the verification is independent of how
the controller was designed. Standard control techniques can be used to the controller was designed. Standard control techniques can be used to
build continuous controllers, and barrier certificates provide a separate build continuous controllers, and barrier certificates provide a separate
check that the result satisfies the required invariants.} check that the result satisfies the required invariants. This also allows for
the checking of control modes with different models than they are designed for.
For example, a lower fidelity model can be used for controller design, but a
higher fidelity model can be used for the actual validation of that stabilizing
controller.
%%% NOTES (Section 4.2): %%% NOTES (Section 4.2):
% - Clarify relationship between barrier certificates and Lyapunov stability % - Clarify relationship between barrier certificates and Lyapunov stability
@ -533,17 +535,12 @@ check that the result satisfies the required invariants.}
\subsubsection{Expulsory Modes} \subsubsection{Expulsory Modes}
The validation of transitory and stabilizing modes hinges on an assumption of Expulsory modes are continuous controllers responsible for
correct plant models. In the case of a mechanical failure, the model will almost
certainly be invalidated. For this reason, we must also build safe shutdown
modes, since a human will not be in the loop to handle failures.
\textcolor{blue}{Expulsory modes are continuous controllers responsible for
ensuring safety when failures occur. They are designed for robustness rather ensuring safety when failures occur. They are designed for robustness rather
than optimality. The control objective is to drive the plant to a safe shutdown than optimality. The control objective is to drive the plant to a safe shutdown
state from potentially anywhere in the state space, under degraded or uncertain state from potentially anywhere in the state space, under degraded or uncertain
dynamics. Examples include emergency core cooling, reactor SCRAM sequences, and dynamics. Examples include emergency core cooling, reactor SCRAM sequences, and
controlled depressurization procedures.} controlled depressurization procedures.
We can detect that physical failures exist because our physical controllers have We can detect that physical failures exist because our physical controllers have
been previously proven correct by reachability and barrier certificates. We know been previously proven correct by reachability and barrier certificates. We know
@ -554,7 +551,7 @@ violated by the continuous physical controller. This is a direct consequence of
having verified the nominal continuous control modes: unexpected behavior having verified the nominal continuous control modes: unexpected behavior
implies off-nominal conditions. implies off-nominal conditions.
\textcolor{blue}{The mathematical formulation for expulsory mode verification The mathematical formulation for expulsory mode verification
differs from transitory modes in two key ways. First, the entry conditions may differs from transitory modes in two key ways. First, the entry conditions may
be the entire state space (or a large, conservatively bounded region) rather be the entire state space (or a large, conservatively bounded region) rather
than a well-defined entry set. The failure may occur at any point during than a well-defined entry set. The failure may occur at any point during
@ -565,7 +562,7 @@ failure modes:
\] \]
where $\Theta_{failure}$ captures the range of possible degraded plant where $\Theta_{failure}$ captures the range of possible degraded plant
behaviors identified through failure mode and effects analysis (FMEA) or behaviors identified through failure mode and effects analysis (FMEA) or
traditional safety analysis.} traditional safety analysis.
We verify expulsory modes using reachability analysis with parametric We verify expulsory modes using reachability analysis with parametric
uncertainty. The verification condition requires that for all parameter values uncertainty. The verification condition requires that for all parameter values
@ -578,12 +575,12 @@ the safe shutdown state:
This is more conservative than nominal reachability, accounting for the fact This is more conservative than nominal reachability, accounting for the fact
that we cannot know exactly which failure mode is active. that we cannot know exactly which failure mode is active.
\textcolor{blue}{Traditional safety analysis techniques inform the construction Traditional safety analysis techniques inform the construction
of $\Theta_{failure}$. Probabilistic risk assessment, FMEA, and design basis of $\Theta_{failure}$. Probabilistic risk assessment, FMEA, and design basis
accident analysis identify credible failure scenarios and their effects on accident analysis identify credible failure scenarios and their effects on
plant dynamics. The expulsory mode must handle the worst-case dynamics within plant dynamics. The expulsory mode must handle the worst-case dynamics within
this envelope. This is where conservative controller design is appropriate: this envelope. This is where conservative controller design is appropriate as
safety margins matter more than performance during emergency shutdown.} safety margins will matter more than performance during emergency shutdown.
%%% NOTES (Section 4.3): %%% NOTES (Section 4.3):
% - Discuss sensor failures vs actual plant failures % - Discuss sensor failures vs actual plant failures
@ -597,40 +594,25 @@ safety margins matter more than performance during emergency shutdown.}
\subsection{Industrial Implementation} \subsection{Industrial Implementation}
\textcolor{blue}{The methodology described above must be validated on realistic The methodology described above must be validated on realistic
systems using industrial-grade hardware to demonstrate practical feasibility. systems using industrial-grade hardware to demonstrate practical feasibility.
This research will leverage the University of Pittsburgh Cyber Energy Center's This research will leverage the University of Pittsburgh Cyber Energy Center's
partnership with Emerson to implement and test the HAHACS methodology on partnership with Emerson to implement and test the HAHACS methodology on
production control equipment.} production control equipment. Emerson's Ovation distributed control system is widely deployed
\textcolor{blue}{Emerson's Ovation distributed control system is widely deployed
in power generation facilities, including nuclear plants. The Ovation platform in power generation facilities, including nuclear plants. The Ovation platform
provides a realistic target for demonstrating that formally synthesized provides a realistic target for demonstrating that formally synthesized
controllers can execute on industrial hardware meeting timing and reliability controllers can execute on industrial hardware meeting timing and reliability
requirements. The discrete automaton produced by reactive synthesis will be requirements. The discrete automaton produced by reactive synthesis will be
compiled to run on Ovation controllers, with verification that the implemented compiled to run on Ovation controllers, with verification that the implemented
behavior matches the synthesized specification exactly.} behavior matches the synthesized specification exactly.
\textcolor{blue}{For the continuous dynamics, we will use a small modular For the continuous dynamics, we will use a small modular
reactor simulation. The SmAHTR (Small modular Advanced High Temperature reactor simulation. The SmAHTR (Small modular Advanced High Temperature
Reactor) model provides a relevant testbed for startup and shutdown procedures. Reactor) model provides a relevant testbed for startup and shutdown procedures.
The ARCADE (Advanced Reactor Control Architecture Development Environment) The ARCADE (Advanced Reactor Control Architecture Development Environment)
interface will establish communication between the Emerson Ovation hardware and interface will establish communication between the Emerson Ovation hardware and
the reactor simulation, enabling hardware-in-the-loop testing of the complete the reactor simulation, enabling hardware-in-the-loop testing of the complete
hybrid controller.} hybrid controller.
\textcolor{blue}{The demonstration will proceed through stages aligned with
Technology Readiness Levels:
\begin{enumerate}
\item \textbf{TRL 3:} Individual components validated in isolation (synthesized
automaton, verified continuous modes)
\item \textbf{TRL 4:} Integrated hybrid controller executing complete sequences
in pure simulation
\item \textbf{TRL 5:} Hardware-in-the-loop testing with Ovation executing the
discrete controller and simulation providing plant response
\end{enumerate}
Success at TRL 5 demonstrates that the methodology produces deployable
controllers, not merely theoretical constructs.}
Working with Emerson on such an implementation is an incredible advantage for Working with Emerson on such an implementation is an incredible advantage for
the success and impact of this work. We will directly address the gap of the success and impact of this work. We will directly address the gap of

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@ -13,15 +13,15 @@
\contentsline {subsubsection}{\numberline {3.2.2}Stabilizing Modes}{12}{}% \contentsline {subsubsection}{\numberline {3.2.2}Stabilizing Modes}{12}{}%
\contentsline {subsubsection}{\numberline {3.2.3}Expulsory Modes}{13}{}% \contentsline {subsubsection}{\numberline {3.2.3}Expulsory Modes}{13}{}%
\contentsline {subsection}{\numberline {3.3}Industrial Implementation}{14}{}% \contentsline {subsection}{\numberline {3.3}Industrial Implementation}{14}{}%
\contentsline {section}{\numberline {4}Metrics for Success}{16}{}% \contentsline {section}{\numberline {4}Metrics for Success}{15}{}%
\contentsline {paragraph}{TRL 3 \textit {Critical Function and Proof of Concept}}{16}{}% \contentsline {paragraph}{TRL 3 \textit {Critical Function and Proof of Concept}}{15}{}%
\contentsline {paragraph}{TRL 4 \textit {Laboratory Testing of Integrated Components}}{16}{}% \contentsline {paragraph}{TRL 4 \textit {Laboratory Testing of Integrated Components}}{15}{}%
\contentsline {paragraph}{TRL 5 \textit {Laboratory Testing in Relevant Environment}}{16}{}% \contentsline {paragraph}{TRL 5 \textit {Laboratory Testing in Relevant Environment}}{15}{}%
\contentsline {section}{\numberline {5}Risks and Contingencies}{18}{}% \contentsline {section}{\numberline {5}Risks and Contingencies}{17}{}%
\contentsline {subsection}{\numberline {5.1}Computational Tractability of Synthesis}{18}{}% \contentsline {subsection}{\numberline {5.1}Computational Tractability of Synthesis}{17}{}%
\contentsline {subsection}{\numberline {5.2}Discrete-Continuous Interface Formalization}{18}{}% \contentsline {subsection}{\numberline {5.2}Discrete-Continuous Interface Formalization}{17}{}%
\contentsline {subsection}{\numberline {5.3}Procedure Formalization Completeness}{19}{}% \contentsline {subsection}{\numberline {5.3}Procedure Formalization Completeness}{18}{}%
\contentsline {section}{\numberline {6}Broader Impacts}{21}{}% \contentsline {section}{\numberline {6}Broader Impacts}{20}{}%
\contentsline {section}{\numberline {7}Schedule, Milestones, and Deliverables}{23}{}% \contentsline {section}{\numberline {7}Schedule, Milestones, and Deliverables}{22}{}%
\contentsline {subsection}{\numberline {7.1}Milestones and Deliverables}{23}{}% \contentsline {subsection}{\numberline {7.1}Milestones and Deliverables}{22}{}%
\contentsline {section}{References}{24}{}% \contentsline {section}{References}{23}{}%