\dasnote{Research statement is very similar to GO because that's what I had
when I prepared it. If it's going to be an executive summary, it should talk
more about the other sections rather than just being a slightly different GO
section.}
% GOAL PARAGRAPH
The goal of this research is to develop a methodology for creating autonomous
hybrid control systems with mathematical 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
their interpretation of plant conditions, they make critical decisions about
when to switch between control objectives.
% Gap
This 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. 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, leveraging the extensive domain knowledge already embedded in
existing operating procedures and safety analyses.
% 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). FRET structures requirements
into scope, condition, component, timing, and response elements. This approach
enables realizability checking that identifies conflicts and ambiguities in
procedures before implementation. Second, we will synthesize discrete mode
switching logic using reactive synthesis to produce deterministic automata that
are correct by construction. Third, we will develop continuous controllers for
each discrete mode using standard control theory and reachability analysis. We
will classify continuous modes based on their transition objectives and verify
safe mode transitions using barrier certificates and reachability analysis.
This compositional approach enables local verification of continuous modes
without requiring global trajectory analysis across the entire hybrid system.
We will validate this methodology through hardware-in-the-loop testing
on an Emerson Ovation distributed control system, made possible through the
University of Pittsburgh Cyber Energy Center's industry partnership.
% Pay-off
This approach enables autonomous management of complex nuclear power operations
while maintaining safety guarantees.

% 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.
    % Outcome
    Control engineers will be able to generate mode-switching
    controllers from regulatory procedures, 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.
    % Outcome
    Without retraining costs or new equipment, control engineers
    will be able to implement high-assurance autonomous controls on industrial
    hardware they already use. 

\end{enumerate}