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
Extensively trained human operators control today's nuclear reactors. Based on plant conditions, these operators follow detailed written procedures and switch between control objectives.
% 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
Operators already work this way: discrete logic switches between continuous control modes. Existing 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. 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, standard control theory designs continuous controllers for each discrete mode, while reachability analysis verifies each controller.

Continuous modes classify by transition objective: transitory modes drive the plant between conditions, stabilizing modes maintain operation within regions, and expulsory modes ensure safety under failures. Assume-guarantee contracts and barrier certificates prove safe mode transitions, enabling local verification without global trajectory analysis. The methodology demonstrates on an Emerson Ovation control system. 
% Pay-off
This autonomous control approach manages complex nuclear power operations 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}