diff --git a/3-research-approach/v3.tex b/3-research-approach/v3.tex index 5ce05f9..9543fa1 100644 --- a/3-research-approach/v3.tex +++ b/3-research-approach/v3.tex @@ -15,22 +15,40 @@ % ---------------------------------------------------------------------------- % 1. INTRODUCTION AND HYBRID SYSTEMS DEFINITION % ---------------------------------------------------------------------------- +Previous approaches to autonomous control have verified +discrete switching logic or continuous control behavior, but not both +simultaneously. Validation of continuous controllers today consists of +extensive simulation trials. Discrete switching logic for routine operation +has been driven by human operators, whose evaluation includes simulated +control room testing and human factors research. Neither method, despite +being extremely resource intensive, provides rigorous guarantees of control +system behavior. HAHACS bridges this gap by composing formal methods from +computer science with control-theoretic verification, formalizing reactor +operations using the framework of hybrid automata. + +The challenge of hybrid system verification lies in the interaction between +discrete and continuous dynamics. Discrete transitions change the governing +vector field, creating discontinuities in the system's behavior. Traditional +verification techniques designed for purely discrete or purely continuous +systems cannot handle this interaction directly.Our methodology addresses this +challenge through decomposition. We verify discrete switching logic and +continuous mode behavior separately, then compose these guarantees to reason +about the complete hybrid system. This two-layer approach mirrors the structure +of reactor operations themselves: discrete supervisory logic determines which +control mode is active, while continuous controllers govern plant behavior +within each mode. To build a high-assurance hybrid autonomous control system (HAHACS), we must first establish a mathematical description of the system. This work draws on -automata theory, temporal logic, and control theory. The nomenclature across -these fields is far from homogeneous, and the reviewer of this proposal is not -expected to be an expert in all of them simultaneously. To present the research -ideas as clearly as possible, the following definitions are provided. - -A hybrid system is a dynamical system that has both continuous and discrete -states. The specific type of system discussed in this proposal is a continuous -autonomous hybrid system. This means that the system does not have external -input and that continuous states do not change instantaneously when discrete -states change. For our systems of interest, the continuous states are physical -quantities that are always Lipschitz continuous. This nomenclature is borrowed -from the Handbook on Hybrid Systems Control, but is redefined here for -convenience: +automata theory, temporal logic, and control theory. A hybrid system is a +dynamical system that has both continuous and discrete states. The specific type +of system discussed in this proposal is a continuous autonomous hybrid system. +This means that the system does not have external input and that continuous +states do not change instantaneously when discrete states change. For our +systems of interest, the continuous states are physical quantities that are +always Lipschitz continuous. This nomenclature is borrowed from the Handbook on +Hybrid Systems Control \cite{HANDBOOK ON HYBRID SYSTEMS}, but is redefined here +for convenience: \begin{equation} H = (\mathcal{Q}, \mathcal{X}, \mathbf{f}, Init, \mathcal{G}, \delta, \mathcal{R}, Inv) @@ -55,46 +73,16 @@ where: The creation of a HAHACS amounts to the construction of such a tuple together with proof artifacts demonstrating that the intended behavior of the control -system is satisfied by its actual implementation. - -\textcolor{blue}{Previous approaches to autonomous control have verified -discrete switching logic or continuous control behavior, but not both -simultaneously. Validation of continuous controllers today consists of -extensive simulation trials. Discrete switching logic for routine operation -has been driven by human operators, whose evaluation includes simulated -control room testing and human factors research. Neither method, despite -being extremely resource intensive, provides rigorous guarantees of control -system behavior. HAHACS bridges this gap by composing formal methods from -computer science with control-theoretic verification, formalizing reactor -operations using the framework of hybrid automata.} - -\textcolor{blue}{The challenge of hybrid system verification lies in the -interaction between discrete and continuous dynamics. Discrete transitions -change the governing vector field, creating discontinuities in the system's -behavior. Traditional verification techniques designed for purely discrete or -purely continuous systems cannot handle this interaction directly.} - -\textcolor{blue}{Our methodology addresses this challenge through decomposition. We verify -discrete switching logic and continuous mode behavior separately, then compose -these guarantees to reason about the complete hybrid system. This two-layer -approach mirrors the structure of reactor operations themselves: discrete -supervisory logic determines which control mode is active, while continuous -controllers govern plant behavior within each mode.} - -\textcolor{blue}{This approach is tractable now because the infrastructure for each component -has matured. Reactive synthesis from temporal logic specifications has -progressed from theoretical results to practical tools; solvers like Strix -can synthesize controllers from LTL specifications in seconds. Reachability -analysis and barrier certificates for continuous systems have decades of -theoretical foundation and modern computational tools. The novelty is not in +system is satisfied by its actual implementation. This approach is tractable now +because the infrastructure for each component has matured. The novelty is not in the individual pieces, but in the architecture that connects them. By defining -entry, exit, and safety conditions at the discrete level first, we transform -the intractable problem of global hybrid verification into a collection of -local verification problems with clear interfaces. Verification is performed -per mode rather than on the full hybrid system, keeping the analysis tractable -even for complex reactor operations.} +entry, exit, and safety conditions at the discrete level first, we transform the +intractable problem of global hybrid verification into a collection of local +verification problems with clear interfaces. Verification is performed per mode +rather than on the full hybrid system, keeping the analysis tractable even for +complex reactor operations. -\begin{figure}[htbp] +\begin{figure} \centering \begin{tikzpicture}[ state/.style={ @@ -113,9 +101,9 @@ even for complex reactor operations.} ] % States \node[state] (q0) at (0,0) {$q_0$\\Cold\\Shutdown}; - \node[state] (q1) at (4,0) {$q_1$\\Heatup}; - \node[state] (q2) at (8,0) {$q_2$\\Power\\Operation}; - \node[state, fill=red!15] (q3) at (4,-3.5) {$q_3$\\SCRAM}; + \node[state] (q1) at (5,0) {$q_1$\\Heatup}; + \node[state] (q2) at (10,0) {$q_2$\\Power\\Operation}; + \node[state, fill=red!15] (q3) at (5,-3.5) {$q_3$\\SCRAM}; % Normal transitions \draw[trans] (q0) -- node[guard, above] {$T_{avg} > T_{min}$} (q1); @@ -133,9 +121,9 @@ even for complex reactor operations.} % Dynamics labels below states \node[dynamics] at (0,-1.4) {$\dot{x} = f_0(x)$}; - \node[dynamics] at (4,-1.4) {$\dot{x} = f_1(x,u)$}; - \node[dynamics] at (8,-1.4) {$\dot{x} = f_2(x,u)$}; - \node[dynamics] at (4,-4.9) {$\dot{x} = f_3(x)$}; + \node[dynamics] at (6,-1.2) {$\dot{x} = f_1(x,u)$}; + \node[dynamics] at (10,-1.4) {$\dot{x} = f_2(x,u)$}; + \node[dynamics] at (5,-4.9) {$\dot{x} = f_3(x)$}; \end{tikzpicture} \caption{Simplified hybrid automaton for reactor startup. Each discrete state @@ -157,54 +145,6 @@ even for complex reactor operations.} % ---------------------------------------------------------------------------- \subsection{System Requirements and Specifications} - -\textcolor{blue}{Before constructing a HAHACS, we must completely describe its -intended behavior. The behavior of any control system originates in -requirements: statements about what the system must do, must not do, and under -what conditions. For nuclear systems, these requirements derive from multiple -sources including regulatory mandates, design basis analyses, and operating -procedures. The challenge is formalizing these requirements with sufficient -precision that they can serve as the foundation for automated controller -synthesis and verification.} - -Autonomous control systems are fundamentally different from automatic control -systems. The difference lies in the level at which they operate. Automatic -control systems are purely operational systems that maintain setpoints or track -references. Autonomous control systems make decisions about which operational -objectives to pursue. - -\begin{figure}[htbp] - \centering - \begin{tikzpicture}[scale=0.8] - % Pyramid layers - \fill[blue!60!black] (0,4) -- (2,4) -- (1,5.5) -- cycle; - \fill[blue!30!white] (-1.5,2.5) -- (3.5,2.5) -- (2,4) -- (0,4) -- cycle; - \fill[blue!15!white] (-3,1) -- (5,1) -- (3.5,2.5) -- (-1.5,2.5) -- cycle; - - % Labels inside pyramid - \node[font=\small\bfseries, white] at (1,4.5) {Strategic}; - \node[font=\small\bfseries] at (1,3.1) {Operational}; - \node[font=\small\bfseries] at (1,1.6) {Tactical}; - - % Descriptions to the right - \node[anchor=west, font=\small, text width=6cm] at (5.5,4.5) - {\textit{Long-term planning:} maintenance scheduling, capacity planning, economic dispatch}; - \node[anchor=west, font=\small, text width=6cm] at (5.5,3.1) - {\textit{Discrete decisions:} startup/shutdown sequences, power level changes, mode transitions}; - \node[anchor=west, font=\small, text width=6cm] at (5.5,1.6) - {\textit{Continuous control:} temperature regulation, pressure control, load following}; - - % Bracket showing HAHACS scope (simple line with text) - \draw[thick] (-3.3,1) -- (-3.5,1) -- (-3.5,4) -- (-3.3,4); - \node[font=\small, align=center, rotate=90] at (-4.2,2.5) {HAHACS scope}; - \end{tikzpicture} - \caption{Control scope hierarchy in nuclear power operations. Strategic control - (long-term planning) remains with human management. HAHACS addresses the - operational level (discrete mode switching) and tactical level (continuous - control within modes), which together form a hybrid control system.} - \label{fig:strat_op_tact} -\end{figure} - Human control of nuclear power can be divided into three different scopes: strategic, operational, and tactical. Strategic control is high-level and long-term decision making for the plant. This level has objectives that are @@ -233,6 +173,51 @@ the continuous evolution of the plant according to the control input and control law, while the operational level is a discrete state evolution that determines which tactical control law to apply. +%Say something about autonomous control systems near here? + +Before constructing a HAHACS, we must completely describe its +intended behavior. The behavior of any control system originates in +requirements: statements about what the system must do, must not do, and under +what conditions. For nuclear systems, these requirements derive from multiple +sources including regulatory mandates, design basis analyses, and operating +procedures. The challenge is formalizing these requirements with sufficient +precision that they can serve as the foundation for autonomous control system +synthesis and verification. + + +\begin{figure} + \centering + \begin{tikzpicture}[scale=0.8] + % Pyramid layers + \fill[blue!30!white] (0,4) -- (2,4) -- (1,5.) -- cycle; + \fill[blue!20!white] (-1.5,2.5) -- (3.5,2.5) -- (2,4) -- (0,4) -- cycle; + \fill[blue!10!white] (-3,1) -- (5,1) -- (3.5,2.5) -- (-1.5,2.5) -- cycle; + + % Labels inside pyramid + \node[font=\small\bfseries] at (1,4.5) {Strategic}; + \node[font=\small\bfseries] at (1,3.1) {Operational}; + \node[font=\small\bfseries] at (1,1.6) {Tactical}; + + % Descriptions to the right + \node[anchor=west, font=\small, text width=8cm] at (5.5,4.6) + {\textit{Long-term planning:} maintenance scheduling, capacity planning, economic dispatch}; + \node[anchor=west, font=\small, text width=8cm] at (5.5,3.1) + {\textit{Discrete decisions:} startup/shutdown sequences, power level changes, mode transitions}; + \node[anchor=west, font=\small, text width=8cm] at (5.5,1.6) + {\textit{Continuous control:} temperature regulation, pressure control, load following}; + + % Bracket showing HAHACS scope (simple line with text) + \draw[thick] (5.0,1.0) -- (-3.5,1) -- (-3.5,4) -- (2.0,4) -- cycle; + \node[font=\small, align=center, rotate=90] at (-4.2,2.5) {HAHACS scope}; + \end{tikzpicture} + \caption{Control scope hierarchy in nuclear power operations. Strategic control + (long-term planning) remains with human management. HAHACS addresses the + operational level (discrete mode switching) and tactical level (continuous + control within modes), which together form a hybrid control system.} + \label{fig:strat_op_tact} +\end{figure} + + This operational control level is the main reason for the requirement of human operators in nuclear control today. The hybrid nature of this control system makes it difficult to prove that a controller will perform according to diff --git a/main.aux b/main.aux index 72007e2..89fdc18 100644 --- a/main.aux +++ b/main.aux @@ -20,18 +20,19 @@ \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.1}HARDENS}{4}{}\protected@file@percent } \citation{Kiniry2024} \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.2}Sequent Calculus and Differential Dynamic Logic}{5}{}\protected@file@percent } +\citation{HANDBOOK ON HYBRID SYSTEMS} \@writefile{toc}{\contentsline {section}{\numberline {3}Research Approach}{7}{}\protected@file@percent } \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Simplified hybrid automaton for reactor startup. Each discrete state $q_i$ has associated continuous dynamics $f_i$. Guard conditions on transitions (e.g., $T_{avg} > T_{min}$) are predicates over continuous state. 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+ diff --git a/main.pdf b/main.pdf index 5801a2c..6b1c44f 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/main.synctex(busy) b/main.synctex(busy) deleted file mode 100644 index e69de29..0000000 diff --git a/main.synctex.gz b/main.synctex.gz index e3339e6..25ce9fd 100644 Binary files a/main.synctex.gz and b/main.synctex.gz differ diff --git a/main.toc b/main.toc index ca84205..88e0011 100644 --- a/main.toc +++ b/main.toc @@ -8,12 +8,12 @@ \contentsline {subsubsection}{\numberline {2.3.2}Sequent Calculus and Differential Dynamic Logic}{5}{}% \contentsline {section}{\numberline {3}Research Approach}{7}{}% \contentsline {subsection}{\numberline {3.1}System Requirements and Specifications}{8}{}% -\contentsline {subsection}{\numberline {3.2}Discrete Controller Synthesis}{11}{}% +\contentsline {subsection}{\numberline {3.2}Discrete Controller Synthesis}{10}{}% \contentsline {subsection}{\numberline {3.3}Continuous Controllers}{11}{}% \contentsline {subsubsection}{\numberline {3.3.1}Transitory Modes}{12}{}% \contentsline {subsubsection}{\numberline {3.3.2}Stabilizing Modes}{13}{}% \contentsline {subsubsection}{\numberline {3.3.3}Expulsory Modes}{14}{}% -\contentsline {subsection}{\numberline {3.4}Industrial Implementation}{15}{}% +\contentsline {subsection}{\numberline {3.4}Industrial Implementation}{14}{}% \contentsline {section}{\numberline {4}Metrics for Success}{16}{}% \contentsline {paragraph}{TRL 3 \textit {Critical Function and Proof of Concept}}{16}{}% \contentsline {paragraph}{TRL 4 \textit {Laboratory Testing of Integrated Components}}{16}{}%