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3-research-approach/v3.tex
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@ -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

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@ -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}{}%