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

% 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 who control them through extensive training, following detailed written procedures and switching between control objectives based on plant conditions.
% Gap
Small modular reactors face a fundamental economic challenge: per-megawatt staffing costs significantly exceed those of conventional plants, threatening economic viability. Autonomous control systems could manage complex operational sequences without constant supervision—but only if they provide assurance equal to or exceeding human-operated systems.

% APPROACH PARAGRAPH Solution
This research combines formal methods from computer science with control theory to produce hybrid control systems correct by construction. 
% Rationale
Human operators already work this way: discrete logic switches between continuous control modes. Formal methods generate provably correct switching logic but fail when continuous dynamics govern transitions. Control theory verifies continuous behavior but cannot prove discrete switching correctness. Both approaches must work together to achieve end-to-end correctness.
% 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 then exposes conflicts and ambiguities before implementation begins. Second, reactive synthesis generates deterministic automata that are provably correct by construction. Third, reachability analysis verifies that continuous controllers—designed using standard control theory—satisfy the requirements that each discrete mode imposes.

Continuous modes classify by control objective. 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 safe mode transitions, enabling local verification without global trajectory analysis. The methodology will demonstrate on an Emerson Ovation control system. 
% Pay-off
This approach manages complex nuclear power operations autonomously while maintaining safety guarantees, directly addressing the economic constraints that threaten 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}