\section{Goals and Outcomes}

% GOAL PARAGRAPH
This research develops autonomous hybrid control systems with mathematical guarantees of safe and correct behavior.

% INTRODUCTORY PARAGRAPH Hook
Nuclear power plants require the highest levels of control system reliability. Control system failures risk economic losses, service interruptions, or radiological release.
% Known information
Nuclear plant operations rely on extensively trained human operators who follow detailed written procedures and strict regulatory requirements. These operators switch between control modes based on plant conditions and procedural guidance.
% Gap
This reliance on human operators prevents autonomous control and creates a fundamental economic challenge for next-generation reactor designs. Small modular reactors face per-megawatt staffing costs far exceeding those of conventional plants, threatening economic viability. The nuclear industry needs autonomous control systems that safely manage complex operational sequences without constant human supervision—systems that provide assurance equal to or exceeding human operators.

% APPROACH PARAGRAPH Solution
Formal methods combine 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 from written requirements but fail when continuous dynamics govern transitions. Control theory verifies continuous behavior but cannot prove discrete switching correctness. No existing approach provides end-to-end correctness guarantees.
% Hypothesis
This approach closes the gap by synthesizing discrete mode transitions directly from written operating procedures and verifying continuous behavior between transitions. Existing procedures formalize into logical specifications. Continuous dynamics verify against transition requirements. The result: autonomous controllers provably free from design defects. 

The University of Pittsburgh Cyber Energy Center provides access to industry collaboration and Emerson control hardware, ensuring solutions align with practical implementation
requirements.

% OUTCOMES PARAGRAPHS
This approach produces three concrete outcomes:

\begin{enumerate}

  % OUTCOME 1 Title
  \item \textbf{Translate written procedures into verified control logic.}
    % Strategy
    We develop a methodology for converting existing written operating
    procedures into formal specifications that can be automatically synthesized
    into discrete control logic. This process uses structured intermediate
    representations to bridge natural language procedures and mathematical
    logic.
    % Outcome
    Control system engineers generate verified mode-switching controllers
    directly from regulatory procedures without formal methods expertise,
    lowering the barrier to high-assurance control systems.

    % OUTCOME 2 Title
  \item \textbf{Verify continuous control behavior across mode transitions.}
    % Strategy
    We establish methods for analyzing continuous control modes to verify
    they satisfy discrete transition requirements. Classical control theory for
    linear systems and reachability analysis for nonlinear dynamics verify
    that each continuous mode reaches its intended transitions safely.
    % 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 \textbf{Demonstrate autonomous reactor startup control with safety
    guarantees.}
    % Strategy
    We apply this methodology to develop an autonomous controller for
    nuclear reactor startup procedures, implementing it on a small modular
    reactor simulation using industry-standard control hardware. This
    demonstration proves correctness across multiple coordinated control
    modes from cold shutdown through criticality to power operation.
    % Outcome
    We demonstrate that autonomous hybrid control can be realized in the
    nuclear industry with current equipment, establishing a path toward reduced
    operator staffing while maintaining safety.

\end{enumerate}

% IMPACT PARAGRAPH Innovation
These three outcomes—procedure translation, continuous verification, and hardware demonstration—establish a complete methodology from regulatory documents to deployed systems.

\textbf{What makes this research new?} This work unifies discrete synthesis with continuous verification to enable end-to-end correctness guarantees for hybrid systems. Formal methods verify discrete logic; control theory verifies continuous dynamics. No existing methodology bridges both with compositional guarantees. This work establishes that bridge by treating discrete specifications as contracts that continuous controllers must satisfy, enabling independent verification of each layer while guaranteeing correct composition.

% Outcome Impact
If successful, control engineers create autonomous controllers from
existing procedures with mathematical proofs of correct behavior. High-assurance
autonomous control becomes practical for safety-critical applications.
% Impact/Pay-off
This capability is essential for the economic viability of next-generation
nuclear power. Small modular reactors offer a promising solution to growing
energy demands, but their success depends on reducing per-megawatt operating
costs through increased autonomy. This research provides the tools to
achieve that autonomy while maintaining the exceptional safety record the
nuclear industry requires.

These three outcomes establish a complete methodology from regulatory documents to deployed systems. This proposal follows the Heilmeier Catechism, with each section explicitly answering its assigned questions:
\begin{itemize}
  \item \textbf{Section 2 (State of the Art):} What has been done? What are the limits of current practice?
  \item \textbf{Section 3 (Research Approach):} What is new? Why will it succeed where prior work has failed?
  \item \textbf{Section 4 (Metrics for Success):} How do we measure success?
  \item \textbf{Section 5 (Risks and Contingencies):} What could prevent success?
  \item \textbf{Section 6 (Broader Impacts):} Who cares? Why now? What difference will it make?
  \item \textbf{Section 8 (Schedule):} How long will it take?
\end{itemize}
Each section begins by stating its Heilmeier questions and ends by summarizing its answers, ensuring both local clarity and global coherence.
