\section{Goals and Outcomes}

% GOAL PARAGRAPH
This research develops a methodology for creating 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,
where failures can result in significant economic losses, service interruptions,
or radiological release.
% Known information
Currently, nuclear plant operations rely on extensively trained human operators
who follow detailed written procedures and strict regulatory requirements to
manage reactor control. These operators make critical decisions about 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 capabilities and
creates a fundamental economic challenge for next-generation reactor designs.
Small modular reactors, in particular, face per-megawatt staffing costs far
exceeding those of conventional plants and threaten their economic viability.

% Critical Need
The nuclear industry needs autonomous control systems that safely manage complex
operational sequences with the same assurance as human-operated systems, but
without constant human supervision.
% APPROACH PARAGRAPH Solution
We will combine formal methods with control theory to build hybrid control
systems that are correct by construction.
% Rationale
Hybrid systems use discrete logic to switch between continuous control modes,
mirroring how operators change control strategies. Existing formal methods
generate provably correct switching logic from written requirements but cannot
handle the continuous dynamics that occur during transitions between modes.
Traditional 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. If existing procedures can be formalized into logical
specifications and continuous dynamics verified against transition requirements,
then autonomous controllers can be built that are provably free from design
defects.
% Pay-off
This approach will enable autonomous control in nuclear power plants while
maintaining the high safety standards required by the industry.

% Qualifications
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 ensure
    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
    iterating to ensure broader system correctness, proving that mode
    transitions 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 to enable end-to-end correctness guarantees for hybrid systems.
While formal methods can verify discrete logic and 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, enabling verification of
each layer independently while guaranteeing correct composition.

% Outcome Impact
If successful, control engineers will create autonomous controllers from
existing procedures with mathematical proof 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.
