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
Nuclear reactors require extensively trained 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 economic viability. Autonomous control systems can manage complex operational sequences without constant supervision—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 build hybrid control systems correct by construction. 
% Rationale
Hybrid systems mirror how operators work: 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. Neither approach provides end-to-end correctness guarantees for hybrid systems.
% 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), which structures requirements into scope, condition, component, timing, and response. Realizability checking identifies conflicts and ambiguities before implementation. Second, reactive synthesis generates deterministic automata—provably correct by construction. Third, standard control theory designs continuous controllers for each discrete mode, which reachability analysis then verifies. Continuous modes classify by transition objectives: 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. An Emerson Ovation control system demonstrates the methodology. 
% 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
If this research is successful, we will be able to do the following:
\begin{enumerate}
  % OUTCOME 1 Title
  \item \textit{Synthesize written procedures into verified control logic.} 
    % Strategy
    We develop a methodology for converting written operating procedures
    into formal specifications. Reactive synthesis tools then generate
    discrete control logic from these specifications.
    % Outcome
    Control engineers can generate mode-switching controllers from regulatory
    procedures with minimal formal methods expertise, reducing 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 provably occur safely and at
    the correct times.

    % OUTCOME 3  Title
  \item \textit{Demonstrate autonomous reactor startup control with safety
    guarantees.}
    % Strategy
    A small modular reactor simulation using industry-standard control hardware
    implements this methodology.
    % 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}