\section{Goals and Outcomes - ORIGINAL}

The goal of this research is to use formal methods to create high-assurance
hybrid control systems. Hybrid control systems have great potential for
autonomous control applications because they can switch between different
control laws based on discrete triggers in the system's operating range. This
approach allows autonomous controllers to use several tractable control laws
optimized for different regions in the state space, rather than relying on a
single controller across the entire operating range. However, the discrete
transitions between control laws in hybrid controllers present significant
challenges in proving stability and liveness properties for the complete system.
While tools from control theory can establish properties for individual control
modes, these guarantees do not generalize when mode switching is introduced.
Existing temporal logic synthesis tools like Strix can generate discrete
controllers from logical specifications, but they assume instantaneous mode
transitions. In hybrid systems, transitions occur along continuous trajectories
governed by differential equations, creating a verification gap that neither
purely discrete synthesis nor traditional control theory can address alone.

This research takes a novel approach to hybrid controller synthesis and
verification by bridging this gap. We will leverage formal methods to create
controllers that are correct-by-construction, enabling guarantees about the
complete system's behavior. To demonstrate this approach, we will develop an
autonomous controller for nuclear power plant start-up procedures. Nuclear power
represents an excellent test case because the continuous reactor dynamics are
well-studied, while the discrete mode switching requirements are explicitly
defined in regulatory procedures and operating guidelines. Current nuclear
reactor control \textit{is} already a hybrid system---many control room
functions employ automated controllers for basic tasks, but the engagement and
selection of these controllers relies on human operators following procedural
decision-making.

The capability to create high-assurance hybrid control systems has significant
potential to reduce labor costs in operating critical systems by removing human
operators from routine control loops. Nuclear power stands to benefit
substantially from increased controller autonomy, as operations and maintenance
represent the largest expense for current reactor designs. While emerging
technologies such as microreactors and small modular reactors will reduce
maintenance costs through factory-manufactured replacement components, they face
increased per-megawatt operating costs if required to maintain traditional
staffing levels. However, if increased autonomy can be safely introduced, these
economic challenges can be addressed while maintaining safety standards.

If this research is successful, we will achieve the following outcomes:

\begin{enumerate}

  \item
    \textbf{Formalize mode switching requirements as logical specifications that
    can be synthesized into discrete controller implementations.} The discrete
    transitions between continuous controller modes are often explicitly defined
    in operating procedures and regulatory requirements for critical systems.
    These natural language requirements will be translated into temporal logic
    specifications, which will then be synthesized into provably correct
    discrete controllers for continuous mode switching.

  \item
    \textbf{Categorize continuous controller modes by their strategic
    relevance.} Different control modes serve distinct purposes: they may be
    transitory (guiding the system toward a target state) or stabilizing
    (maintaining the system within desired operating bounds). While the discrete
    component handles mode switching decisions, this outcome will identify the
    dynamic properties that continuous components must satisfy for each
    controller mode.

  \item
    \textbf{Verify that continuous controller modes satisfy dynamic
    requirements using appropriate analysis methods.} For linear dynamics, we
    will apply classical control theory to establish stability and performance
    within each mode. For nonlinear systems, reachability analysis will verify
    that transitory modes drive the system toward intended transitions while
    maintaining safety constraints, and that stabilizing modes maintain the
    system within designated operating regions.

  \item
    \textbf{Prove that hybrid system implementations achieve strategic goals
    across the complete operating range.} By synthesizing discrete controller
    transitions from logical specifications using correct-by-construction
    methods and verifying that continuous components perform appropriately
    between discrete transitions, we can establish confidence that the hybrid
    system is defect-free and suitable for deployment as a critical autonomous
    controller.
  
\end{enumerate}