A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems

As autonomous systems become more ubiquitous in daily life, ensuring high performance with guaranteed safety is crucial. However, safety and performance could be competing objectives, which makes their co-optimization difficult. Learning-based methods, such as Constrained Reinforcement Learning (CRL), achieve strong performance but lack formal safety guarantees due to safety being enforced as soft constraints, limiting their use in safety-critical settings. Conversely, formal methods such as Hamilton-Jacobi (HJ) Reachability Analysis and Control Barrier Functions (CBFs) provide rigorous safety assurances but often neglect performance, resulting in overly conservative controllers. To bridge this gap, we formulate the co-optimization of safety and performance as a state-constrained optimal control problem, where performance objectives are encoded via a cost function and safety requirements are imposed as state constraints. We demonstrate that the resultant value function satisfies a Hamilton-Jacobi-Bellman (HJB) equation, which we approximate efficiently using a novel physics-informed machine learning framework. In addition, we introduce a conformal prediction-based verification strategy to quantify the learning errors, recovering a high-confidence safety value function, along with a probabilistic error bound on performance degradation. Through several case studies, we demonstrate the efficacy of the proposed framework in enabling scalable learning of safe and performant controllers for complex, high-dimensional autonomous systems.

Autonomous systems—like self-driving cars and drones—are becoming more common in our daily lives. For these systems to be trustworthy, they must not only perform well but also operate safely at all times. However, making a system both safe and high-performing is challenging because these goals often conflict. Some learning-based approaches allow these systems to perform very well, but they don’t always guarantee safety. On the other hand, mathematical techniques that ensure safety often make the system too conservative. Our research combines the best of both worlds: it uses physics informed machine learning to learn how to control these systems safely while still allowing them to perform well. We also include a way to measure how confident we are in the safety of our system, even when the controller is learned from data. This helps make sure the system won't fail in real-world situations. We test our approach in several examples and show that it works effectively, even for complex systems.