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

• URL: http://arxiv.org/abs/2502.11057v1
• Date: Sun, 16 Feb 2025 09:46:17 GMT
• Title: A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems
• Authors: Manan Tayal, Aditya Singh, Shishir Kolathaya, Somil Bansal,
• Abstract summary: Safety and performance could be competing objectives, which makes their co-optimization difficult. We propose 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 equation, which we approximate efficiently using a novel machine learning framework.
• Score: 8.347548017994178
• License:
• Abstract: 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.

Related papers

• Learning-Enhanced Safeguard Control for High-Relative-Degree Systems: Robust Optimization under Disturbances and Faults [6.535600892275023]
  This paper aims to enhance system performance with safety guarantee in reinforcement learning-based optimal control problems. The concept of gradient similarity is proposed to quantify the relationship between the gradient of safety and the gradient of performance. gradient manipulation and adaptive mechanisms are introduced in the safe RL framework to enhance the performance with a safety guarantee.
  arXiv  Detail & Related papers  (2025-01-26T03:03:02Z)
• Evaluating Model-free Reinforcement Learning toward Safety-critical Tasks [70.76757529955577]
  This paper revisits prior work in this scope from the perspective of state-wise safe RL. We propose Unrolling Safety Layer (USL), a joint method that combines safety optimization and safety projection. To facilitate further research in this area, we reproduce related algorithms in a unified pipeline and incorporate them into SafeRL-Kit.
  arXiv  Detail & Related papers  (2022-12-12T06:30:17Z)
• Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environments [84.3830478851369]
  We propose a safe reinforcement learning approach that can jointly learn the environment and optimize the control policy. Our approach can effectively enforce hard safety constraints and significantly outperform CMDP-based baseline methods in system safe rate measured via simulations.
  arXiv  Detail & Related papers  (2022-09-29T20:49:25Z)
• Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions [60.26921219698514]
  We introduce a model-uncertainty-aware reformulation of CBF-based safety-critical controllers. We then present the pointwise feasibility conditions of the resulting safety controller. We use these conditions to devise an event-triggered online data collection strategy.
  arXiv  Detail & Related papers  (2022-08-23T05:02:09Z)
• Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functions [35.9713619595494]
  Reinforcement Learning and continuous nonlinear control have been successfully deployed in multiple domains of complicated sequential decision-making tasks. Given the exploration nature of the learning process and the presence of model uncertainty, it is challenging to apply them to safety-critical control tasks. We propose a emphprovably efficient episodic safe learning framework for online control tasks.
  arXiv  Detail & Related papers  (2022-07-29T00:54:35Z)
• Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learning [24.56889192688925]
  Reach-avoid optimal control problems are central to safety and liveness assurance for autonomous robotic systems. Recent successes in reinforcement learning methods to approximately solve optimal control problems with performance objectives make their application to certification problems attractive. Recent work has shown promise in extending the reinforcement learning machinery to handle safety-type problems, whose objective is not a sum, but a minimum (or maximum) over time.
  arXiv  Detail & Related papers  (2021-12-23T00:44:38Z)
• Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty [77.18483084440182]
  Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. We present a Gaussian Process (GP)-based approach to tackle the problem of model uncertainty in safety-critical controllers that use CBFs and CLFs.
  arXiv  Detail & Related papers  (2021-06-13T23:08:49Z)
• Closing the Closed-Loop Distribution Shift in Safe Imitation Learning [80.05727171757454]
  We treat safe optimization-based control strategies as experts in an imitation learning problem. We train a learned policy that can be cheaply evaluated at run-time and that provably satisfies the same safety guarantees as the expert.
  arXiv  Detail & Related papers  (2021-02-18T05:11:41Z)
• Learning Robust Hybrid Control Barrier Functions for Uncertain Systems [68.30783663518821]
  We propose robust hybrid control barrier functions as a means to synthesize control laws that ensure robust safety. Based on this notion, we formulate an optimization problem for learning robust hybrid control barrier functions from data. Our techniques allow us to safely expand the region of attraction of a compass gait walker that is subject to model uncertainty.
  arXiv  Detail & Related papers  (2021-01-16T17:53:35Z)
• Neural Lyapunov Redesign [36.2939747271983]
  Learning controllers must guarantee some notion of safety to ensure that it does not harm either the agent or the environment. Lyapunov functions are effective tools to assess stability in nonlinear dynamical systems. We propose a two-player collaborative algorithm that alternates between estimating a Lyapunov function and deriving a controller that gradually enlarges the stability region.
  arXiv  Detail & Related papers  (2020-06-06T19:22:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.