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 operate under the control of extensively trained human operators who 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 offer a solution—they 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 that are correct by construction. 
% Rationale
This approach mirrors how operators already work: discrete logic switches between continuous control modes. Existing formal methods can generate provably correct switching logic, but they fail when continuous dynamics govern transitions. Control theory verifies continuous behavior, but it 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, written operating procedures translate into temporal logic specifications using NASA's Formal Requirements Elicitation Tool (FRET). FRET structures requirements into scope, condition, component, timing, and response. Conflicts and ambiguities emerge through realizability checking—before implementation begins. Second, reactive synthesis generates deterministic automata provably correct by construction. Third, standard control theory designs continuous controllers for each discrete mode. Reachability analysis then verifies each controller. Transition objectives classify continuous modes. Transitory modes drive the plant between conditions. Stabilizing modes maintain operation within regions. Expulsory modes ensure safety under failures. Assume-guarantee contracts and barrier certificates prove safe mode transitions. This enables 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. It directly addresses 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}