\section{Goals and Outcomes}

% GOAL PARAGRAPH
This research develops a methodology for creating autonomous hybrid control
systems that provide mathematical guarantees of safe and correct behavior.

% INTRODUCTORY PARAGRAPH Hook
Nuclear power plants require the highest levels of control system reliability.
Control system failures cause significant 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 to
manage reactor control. These operators decide when to
switch between different control modes based on their interpretation of 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 their economic viability.
The nuclear industry therefore needs autonomous control systems that safely manage complex
operational sequences without constant human supervision while maintaining
higher assurance than human-operated systems.

% APPROACH PARAGRAPH Solution
We combine formal methods with control theory to build hybrid control
systems that are 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 cannot
handle the continuous dynamics during transitions between modes.
Control theory verifies continuous behavior but lacks tools for
proving correctness of discrete switching decisions. This gap between discrete
and continuous verification prevents end-to-end correctness guarantees.
% Hypothesis
Our approach closes this gap by synthesizing discrete mode transitions directly
from written operating procedures and verifying continuous behavior between
transitions. We formalize existing procedures into logical
specifications and verify continuous dynamics against transition requirements,
enabling autonomous controllers provably free from design
defects. This work is conducted within the University of Pittsburgh Cyber Energy Center,
which provides access to industry collaboration and Emerson control hardware,
ensuring that developed solutions align with practical implementation
requirements.

% OUTCOMES PARAGRAPHS
If this research is successful, we will be able to do the following:

\begin{enumerate}

  % OUTCOME 1 Title
  \item \textbf{Translate written procedures into verified control logic.}
    % Strategy
    We will develop a methodology for converting existing written operating
    procedures into formal specifications that can be automatically synthesized
    into discrete control logic. This process will use structured intermediate
    representations to bridge natural language procedures and mathematical
    logic.
    % Outcome
    Control system engineers will 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 will 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 will verify
    that each continuous mode safely reaches its intended transitions.
    % Outcome
    Engineers will design continuous controllers using standard practices while
    maintaining formal correctness guarantees. Mode transitions will provably occur safely and at the correct times.

    % OUTCOME 3  Title
  \item \textbf{Demonstrate autonomous reactor startup control with safety
    guarantees.}
    % Strategy
    We will 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 will prove correctness across multiple coordinated control
    modes from cold shutdown through criticality to power operation.
    % Outcome
    We will 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—together establish a complete methodology from regulatory documents to deployed systems.

\textbf{The key innovation} unifies discrete synthesis with continuous verification, enabling end-to-end correctness guarantees for hybrid systems.
Formal methods can verify discrete logic. Control theory can verify
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. This enables independent
verification of each layer while guaranteeing correct composition.

% Outcome Impact
If successful, control engineers will create autonomous controllers from
existing procedures with mathematical proofs of correct behavior. High-assurance
autonomous control will become 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 will provide the tools to
achieve that autonomy while maintaining the exceptional safety record the
nuclear industry requires.