\section*{Formal Synthesis of Hybrid Controllers for Nuclear Power}
\subsection*{PI: Dane Sabo, NRC Fellow, University of Pittsburgh \\\today}
% GOAL PARAGRAPH
The goal of this research is to develop a methodology for creating autonomous
hybrid control systems with 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. Currently, nuclear power relies on extensively trained
operators who follow detailed written procedures to manage reactor control.
These operators make critical decisions about when to switch between control
objectives based on their interpretation of plant conditions and procedural guidance. 
% Gap
However, this reliance on human operators prevents autonomous control and
creates an economic challenge for next-generation nuclear power plants. Small modular
reactors face significantly higher per-megawatt staffing costs than conventional
plants, threatening their economic viability. Autonomous control systems are
needed that can safely manage complex operational sequences with the same
assurance as human-operated systems, but without constant supervision.

% APPROACH PARAGRAPH Solution
To address this need, 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 dynamic modes,
similar to how operators change control strategies. Existing formal methods can
generate provably correct switching logic with reactive synthesis, but cannot
incorporate continuous dynamics or hybrid system transitions. Traditional
control theory verifies continuous behavior but lacks tools for proving discrete
switching correctness. 
% Hypothesis
We will combine tools from these two fields to build autonomous hybrid control
systems that are correct by construction. We will formalize existing procedures
into logical specifications and verify that continuous dynamics satisfy
transition requirements between discrete modes.  
% Pay-off
This approach will enable autonomous control in nuclear power plants while
maintaining required safety standards.

\vspace{11pt}
% OUTCOMES PARAGRAPHS
If this research is successful, we will be able to do the following:

\begin{enumerate}

  % OUTCOME 1 Title
  \item \textbf{Synthesize written procedures into verified control logic.} 
    % Strategy
    We will develop a methodology for converting written operating procedures
    into formal specifications. These specifications can be automatically
    synthesized into discrete control logic using reactive synthesis tools. This
    process uses structured intermediate representations to bridge natural
    language and mathematical logic. 
    % Outcome
    Control engineers will be able to generate verified mode-switching controllers 
    from regulatory procedures with little formal methods expertise, reducing
    barriers 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. Using classical control
    theory for linear systems and reachability analysis for nonlinear dynamics,
    we verify each continuous mode safely reaches intended transitions. 
    % Outcome
    Engineers will be able to design continuous controllers using standard practices while
    ensuring system correctness and proving mode transitions occur safely at the
    right 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. We will implement this methodology on a small modular reactor
    simulation using industry-standard control hardware. This trial will include
    multiple coordinated control modes from cold shutdown through
    criticality to power operation. 
    % Outcome
    This will provide evidence that autonomous hybrid control can be realized with
    current equipment, establishing a path toward reducing operator staffing
    while maintaining safety.

\end{enumerate}

% IMPACT PARAGRAPH Innovation
The innovation is unifying discrete synthesis and continuous verification to
enable end-to-end correctness guarantees for hybrid systems. 
% Outcome Impact
If successful, control engineers will be able to create autonomous controllers from existing
procedures with mathematical proof of correct behavior, making high-assurance
autonomous control practical for safety-critical applications. 
% Impact/Pay-off
This capability is essential for economic viability of next-generation nuclear
power. Small modular reactors represent a promising solution to growing energy
demands, but 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 required by the nuclear industry.
