\section{Goals and Outcomes} % 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 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— such as transitioning from startup heating to power operation—based on their interpretation of plant conditions and procedural guidance. % Gap However, this reliance on human operators prevents the introduction of autonomous control capabilities and creates a fundamental economic challenge for next-generation reactor designs. Emerging technologies like small modular reactors face significantly higher per-megawatt staffing costs than conventional plants, threatening their economic viability. % Critical Need What is needed is a way to create autonomous control systems that can safely manage complex operational sequences with the same level of assurance as human-operated systems, but without requiring constant human 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 can generate provably correct switching logic from written requirements, but they cannot handle the continuous dynamics that occur during transitions between modes. Meanwhile, traditional control theory can verify continuous behavior but lacks tools for proving correctness of discrete switching decisions. % Hypothesis By synthesizing discrete mode transitions directly from written operating procedures and verifying continuous behavior between transitions, we can create hybrid control systems with end-to-end correctness guarantees. If we can formalize existing procedures into logical specifications and verify that continuous dynamics satisfy transition requirements, then we can build autonomous controllers 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 solutions developed are aligned 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 be able to generate verified mode-switching controllers directly from regulatory procedures without requiring expertise in formal methods, reducing the barrier to creating 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 the discrete transition requirements. Using a combination of classical control theory for linear systems and reachability analysis for nonlinear dynamics, we will verify that each continuous mode can safely reach its intended transitions. % Outcome Engineers will be able to design continuous controllers using standard practices while iterating to ensure broader system correctness, proving that mode transitions occur safely and 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 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 provide evidence that autonomous hybrid control can be realized in the nuclear industry with current control equipment, establishing a path toward reducing operator staffing requirements while maintaining safety. \end{enumerate} % IMPACT PARAGRAPH Innovation The innovation in this work is the unification of 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 the economic viability of next-generation nuclear power. Small modular reactors represent 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 required by the nuclear industry.