Thesis/1-goals-and-outcomes/research_statement_v1.tex

% GOAL PARAGRAPH
I develop autonomous control systems that guarantee safe and correct behavior through mathematical proof.

% INTRODUCTORY PARAGRAPH Hook
Nuclear reactors today depend on extensively trained human operators. These operators follow detailed written procedures and switch between control objectives as plant conditions change.
% Gap
Small modular reactors face a fundamental economic challenge: their per-megawatt staffing costs significantly exceed those of conventional plants. This cost disparity threatens economic viability. Autonomous control could manage complex operational sequences without constant supervision—but only if safety assurance equals or exceeds that of human operators.

% APPROACH PARAGRAPH Solution
I produce hybrid control systems that are correct by construction. This work unifies formal methods from computer science with control theory. 
% Rationale
Human operators already work this way: discrete logic switches between continuous control modes. Formal methods generate provably correct switching logic but cannot handle continuous dynamics. Control theory verifies continuous behavior but cannot prove discrete switching correctness. 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. FRET structures 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. Engineers design these continuous controllers using standard control theory techniques.

Control objectives classify continuous modes into three types. Transitory modes drive the plant between conditions. Stabilizing modes maintain operation within regions. Expulsory modes ensure safety under failures. Barrier certificates and assume-guarantee contracts prove mode transitions are safe. This enables local verification without global trajectory analysis. I demonstrate this methodology on an Emerson Ovation control system—the industrial platform nuclear power plants already use.
% Pay-off
This approach manages complex nuclear power operations autonomously while maintaining safety guarantees. It directly addresses 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 with minimal formal methods expertise. 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}