\section{Goals and Outcomes}

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

% INTRODUCTORY PARAGRAPH Hook
Nuclear power plants demand the highest levels of control system reliability. Control system failures risk economic losses, service interruptions, or radiological release.
% Known information
Extensively trained human operators control nuclear plants today by following 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 their economic viability. Autonomous control offers a solution—managing 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 research unifies formal methods with control theory to produce hybrid control systems correct by construction.
% Rationale
Human operators already work this way: they use discrete logic to switch between continuous control modes. Formal methods generate provably correct switching logic from written requirements but cannot verify continuous dynamics. Control theory verifies continuous behavior but cannot prove discrete switching correctness. Both are required for end-to-end correctness.
% 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. Together, these steps transform operating procedures into logical specifications constraining 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
    The 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 engineers can 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
\textbf{What makes this research new?} No existing methodology achieves end-to-end correctness guarantees for hybrid systems. Section 2 shows that prior work verified discrete logic or continuous dynamics—never both compositionally. 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. Control theory verifies continuous dynamics. Together, these three outcomes—procedure translation, continuous verification, and hardware demonstration—establish a complete methodology spanning from regulatory documents to deployed systems.

% Outcome Impact
If successful, control engineers will create autonomous controllers from existing procedures with mathematical proofs of correct behavior. This makes high-assurance autonomous control practical for safety-critical applications—a capability essential for the economic viability of next-generation nuclear power. Small modular reactors offer a promising solution to growing energy demands. 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.
