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

% INTRODUCTORY PARAGRAPH Hook
Today's nuclear reactors depend on human operators with extensive training. These operators follow detailed written procedures and switch between control objectives based on plant conditions.
% Gap
Small modular reactors face a fundamental economic challenge: their per-megawatt staffing costs significantly exceed those of conventional plants, threatening their economic viability. Autonomous control systems could manage complex operational sequences without constant supervision—but only with assurance equal to or exceeding human-operated systems.

% APPROACH PARAGRAPH Solution
This research produces hybrid control systems correct by construction, combining formal methods from computer science with control theory. 
% Rationale
Human operators already work this way: discrete logic switches between continuous control modes. Formal methods alone fail because they generate provably correct switching logic but cannot handle the continuous dynamics governing transitions. Control theory alone also fails because it verifies continuous behavior but cannot prove discrete switching correctness. Achieving end-to-end correctness requires both approaches working together.
% Hypothesis and Technical Approach
Three stages bridge this gap. First, NASA's Formal Requirements Elicitation Tool (FRET) translates written operating procedures into temporal logic specifications, structuring requirements by scope, condition, component, timing, and response. Realizability checking exposes conflicts and ambiguities before implementation begins. Second, reactive synthesis generates deterministic automata provably correct by construction. Third, reachability analysis verifies that continuous controllers satisfy the requirements each discrete mode imposes. Standard control theory techniques design these continuous controllers.

Control objectives classify continuous modes into three types: transitory modes drive the plant between conditions, stabilizing modes maintain operation within regions, and expulsory modes ensure safety under failures. Barrier certificates and assume-guarantee contracts prove safe mode transitions, enabling local verification without global trajectory analysis. An Emerson Ovation control system will demonstrate the methodology.
% Pay-off
This approach manages complex nuclear power operations autonomously while maintaining safety guarantees, directly addressing the economic constraints threatening small modular reactor viability.

% OUTCOMES PARAGRAPHS
This research, if successful, produces three concrete outcomes:
\begin{enumerate}
  % OUTCOME 1 Title
  \item \textit{Synthesize written procedures into verified control logic.} 
    % Strategy
    A methodology converts written operating procedures into formal specifications.
    Reactive synthesis tools then generate discrete control logic from these specifications.
    % Outcome
    Control engineers generate mode-switching controllers directly from regulatory
    procedures. Minimal formal methods expertise required. This reduces barriers to
    high-assurance control systems.

    % OUTCOME 2 Title
  \item \textit{Verify continuous control behavior across mode transitions.}
    % Strategy
    Reachability analysis verifies that continuous control modes satisfy discrete
    transition requirements. 
    % 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 \textit{Demonstrate autonomous reactor startup control with safety
    guarantees.}
    % Strategy
    This methodology demonstrates on a small modular reactor simulation using industry-standard control hardware.
    % Outcome
    Control engineers implement high-assurance autonomous controls on
    industrial platforms they already use, enabling autonomy without retraining
    costs or new equipment development.

\end{enumerate}