\section*{Formal Synthesis of Hybrid Controllers for Nuclear Power}
\subsection*{PI: Dane Sabo, NRC Fellow, University of Pittsburgh}
% GOAL PARAGRAPH
The goal of this research is to develop a methodology for creating autonomous
control systems with event-driven control laws that have guarantees of safe and
correct behavior.

% INTRODUCTORY PARAGRAPH Hook
Nuclear power relies on extensively trained operators who follow detailed
written procedures to manage reactor control. Based on these procedures and
operators' interpretation of plant conditions, operators make critical decisions
about when to switch between control objectives. 
% Gap
While human operators have maintained the nuclear industry's exceptional safety
record, reliance on human operators has created 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 from computer science 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,
similar to how operators change control strategies. Existing formal methods
generate provably correct switching logic but cannot handle continuous dynamics
during transitions, while traditional control theory verifies continuous
behavior but lacks tools for proving discrete switching correctness. 
% Hypothesis and Technical Approach
We will bridge this gap through a three-stage methodology. First, we will
translate written operating procedures into temporal logic specifications using
NASA's Formal Requirements Elicitation Tool (FRET), which structures
requirements into scope, condition, component, timing, and response elements.
This structured approach enables realizability checking to identify conflicts
and ambiguities in procedures before implementation. Second, we will synthesize
discrete mode switching logic from these specifications using reactive synthesis
tools such as Strix, which generates deterministic automata that are provably
correct by construction. Third, we will develop and verify continuous
controllers for each discrete mode using standard control theory and
reachability analysis. We will classify continuous modes based on their
transition objectives, and then employ assume-guarantee contracts and barrier
certificates to prove that mode transitions occur safely and as defined by the
deterministic automata. This compositional approach enables local verification
of continuous modes without requiring global trajectory analysis across the
entire hybrid system. We will demonstrate this methodology by developing an
autonomous startup controller for a Small Modular Advanced High Temperature
Reactor (SmAHTR) and implementing it on an Emerson Ovation control system using
the ARCADE hardware-in-the-loop platform. 
% Pay-off
This approach will demonstrate autonomous control can be used for complex
nuclear power operations while maintaining safety guarantees.

\vspace{11pt}

% 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 will develop a methodology for converting written operating procedures
    into formal specifications. These specifications will be 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 mode-switching controllers from
    regulatory procedures with little formal methods expertise, reducing
    barriers to high-assurance control systems.

    % OUTCOME 2 Title
  \item \textit{Verify continuous control behavior across mode transitions. }
    % Strategy
    We will develop methods using reachability analysis to ensure continuous control modes 
    satisfy discrete transition requirements. 
    % 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 \textit{Demonstrate autonomous reactor startup control with safety
    guarantees. }
    % Strategy
    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 on a SmAHTR reactor simulation in a hardware-in-the-loop
    experiment. 
    % Outcome
    Control engineers will be able to implement high-assurance autonomous
    controls on industrial platforms they already use, enabling users to
    achieve autonomy without retraining costs or developing new equipment.

\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.
