\section{Goals and Outcomes} % GOAL PARAGRAPH This research develops 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. Control system failures risk 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. When operators switch between different control modes, plant conditions and procedural guidance inform their decisions. % 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 that far exceed those of conventional plants, threatening their economic viability. The nuclear industry needs autonomous control systems that manage complex operational sequences safely without constant human supervision while providing assurance equal to or exceeding human-operated systems. % APPROACH PARAGRAPH Solution We combine formal methods with control theory to build hybrid control systems 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 continuous dynamics during transitions between modes. Control theory verifies continuous behavior but cannot prove correctness of discrete switching decisions. This gap 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. This approach produces autonomous controllers provably free from design defects. We conduct this work within the University of Pittsburgh Cyber Energy Center, which provides access to industry collaboration and Emerson control hardware. Solutions developed here therefore 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 develop a methodology for converting existing written operating procedures into formal specifications that can be automatically synthesized into discrete control logic. This process uses structured intermediate representations to bridge natural language procedures and mathematical logic. % Outcome Control system engineers 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 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 verify that each continuous mode reaches its intended transitions safely. % Outcome Engineers design continuous controllers using standard practices while maintaining formal correctness guarantees. Mode transitions occur safely and at the correct times, provably. % OUTCOME 3 Title \item \textbf{Demonstrate autonomous reactor startup control with safety guarantees.} % Strategy We 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 proves correctness across multiple coordinated control modes from cold shutdown through criticality to power operation. % Outcome We 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—establish a complete methodology from regulatory documents to deployed systems. \textbf{What is new:} We unify discrete synthesis with continuous verification to enable end-to-end correctness guarantees for hybrid systems. Formal methods verify discrete logic. Control theory verifies 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 independent verification of each layer while guaranteeing correct composition. % Outcome Impact If successful, control engineers create autonomous controllers from existing procedures with mathematical proofs of correct behavior. High-assurance autonomous control becomes 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 provides the tools to achieve that autonomy while maintaining the exceptional safety record the nuclear industry requires. The following sections systematically answer the Heilmeier Catechism questions that define this research: Section 2 examines the state of the art, establishing what has been done and what remains impossible with current approaches. Section 3 presents our hybrid control synthesis methodology, demonstrating what is new and why it will succeed where prior work has not. Section 4 defines how we measure success through Technology Readiness Level advancement from analytical concepts to hardware demonstration. Section 5 identifies risks that could prevent success and establishes contingencies. Section 6 addresses who cares and why now, examining the economic imperative driving autonomous nuclear control and the broader impact on safety-critical systems. Section 7 provides the research schedule and deliverables, answering how long this work will take.