\section{Goals and Outcomes}

% GOAL PARAGRAPH
This research develops autonomous hybrid control systems with mathematical guarantees of safe and correct behavior.

% INTRODUCTORY PARAGRAPH Hook
Nuclear power plants require the highest levels of control system reliability. Control system failures risk economic losses, service interruptions, or radiological release.
% Known information
Nuclear plants today depend on extensively trained human operators. These operators follow detailed written procedures and strict regulatory requirements. They switch between control modes based on plant conditions and procedural guidance.
% Gap
This reliance on human operators prevents autonomous control and creates a fundamental economic challenge for next-generation reactor designs. Small modular reactors face per-megawatt staffing costs far exceeding those of conventional plants, threatening economic viability. Autonomous control could manage complex operational sequences without constant supervision—but only if it provides safety assurance equal to or exceeding that of human operators.

% APPROACH PARAGRAPH Solution
This work unifies formal methods with control theory. This produces hybrid control systems that are correct by construction.
% Rationale
Human operators already work this way: discrete logic switches between continuous control modes. Formal methods generate provably correct switching logic from written requirements but cannot handle the continuous dynamics governing transitions. Control theory verifies continuous behavior but cannot prove discrete switching correctness. End-to-end correctness requires both.
% Hypothesis
Two steps close this gap. First, reactive synthesis generates discrete mode transitions directly from written operating procedures. Second, reachability analysis verifies continuous behavior against discrete requirements. This approach transforms operating procedures into logical specifications that constrain continuous dynamics—producing autonomous controllers provably free from design defects. 

The University of Pittsburgh Cyber Energy Center provides access to industry collaboration and Emerson control hardware, ensuring solutions align with practical implementation requirements.

% OUTCOMES PARAGRAPHS
If successful, this approach produces three concrete outcomes:

\begin{enumerate}

  % OUTCOME 1 Title
  \item \textbf{Translate written procedures into verified control logic.}
    % Strategy
    A methodology converts written operating procedures into formal
    specifications. Reactive synthesis tools then automatically generate
    discrete control logic from these specifications. Structured intermediate
    representations bridge natural language procedures and mathematical logic.
    % Outcome
    Control system engineers generate verified mode-switching controllers
    directly from regulatory procedures without formal methods expertise,
    lowering the barrier to high-assurance control systems.

    % OUTCOME 2 Title
  \item \textbf{Verify continuous control behavior across mode transitions.}
    % Strategy
    Methods for analyzing continuous control modes verify that they satisfy
    discrete transition requirements. Classical control theory handles linear
    systems, while reachability analysis handles nonlinear dynamics. Both verify that
    each continuous mode reaches its intended transitions safely.
    % Outcome
    Engineers design continuous controllers using standard practices while maintaining formal correctness guarantees. Mode transitions occur safely and at the correct times—provably.

    % OUTCOME 3  Title
  \item \textbf{Demonstrate autonomous reactor startup control with safety
    guarantees.}
    % Strategy
    This methodology applies to autonomous nuclear reactor startup procedures,
    demonstrating on a small modular reactor simulation using industry-standard
    control hardware. The demonstration proves correctness across multiple
    coordinated control modes from cold shutdown through criticality to power operation.
    % Outcome
    Autonomous hybrid control becomes realizable in the nuclear industry with
    current equipment, establishing a path toward reduced operator staffing
    while maintaining safety.

\end{enumerate}

% IMPACT PARAGRAPH Innovation
These three outcomes—procedure translation, continuous verification, and hardware demonstration—establish a complete methodology from regulatory documents to deployed systems.

\textbf{What makes this research new?} No existing methodology achieves end-to-end correctness guarantees for hybrid systems. This work unifies discrete synthesis with continuous verification through a key innovation: discrete specifications become contracts that continuous controllers must satisfy. Each layer verifies independently while guaranteeing correct composition—formal methods verify discrete logic, while control theory verifies continuous dynamics.

% Outcome Impact
If successful, control engineers will create autonomous controllers from existing procedures with mathematical proofs of correct behavior, making high-assurance autonomous control practical for safety-critical applications. This capability is essential for the economic viability of next-generation nuclear power. Small modular reactors, in particular, offer a promising solution to growing energy demands, but their success depends on reducing per-megawatt operating costs through increased autonomy. This research provides the tools to achieve that autonomy while maintaining the exceptional safety record the nuclear industry requires. 

This proposal follows the Heilmeier Catechism. Each section explicitly answers its assigned questions:
\begin{itemize}
  \item \textbf{Section 2 (State of the Art):} What has been done? What are the limits of current practice?
  \item \textbf{Section 3 (Research Approach):} What is new? Why will it succeed?
  \item \textbf{Section 4 (Metrics for Success):} How will success be measured?
  \item \textbf{Section 5 (Risks and Contingencies):} What could prevent success?
  \item \textbf{Section 6 (Broader Impacts):} Who cares? Why now? What difference will it make?
  \item \textbf{Section 8 (Schedule):} How long will it take?
\end{itemize}
Each section begins by stating its Heilmeier questions and ends by summarizing its answers. This ensures both local clarity and global coherence.
