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This paper proposes the Phy-DRL: a physics-regulated deep reinforcement learning (DRL) framework for safety-critical autonomous systems. The Phy-DRL has three distinguished invariant-embedding designs: i) residual action policy (i.e., integrating data-driven-DRL action policy and physics-model-based action policy), ii) automatically constructed safety-embedded reward, and iii) physics-model-guided neural network (NN) editing, including link editing and activation editing. Theoretically, the Phy-DRL exhibits 1) a mathematically provable safety guarantee and 2) strict compliance of critic and actor networks with physics knowledge about the action-value function and action policy. Finally, we evaluate the Phy-DRL on a cart-pole system and a quadruped robot. The experiments validate our theoretical results and demonstrate that Phy-DRL features guarantee safety compared to purely data-driven DRL and solely model-based design, while offering remarkably fewer learning parameters and fast training towards safety guarantee. 

Deep reinforcement learning (DRL) has demonstrated impressive success in solving complex control tasks by synthesizing control policies from data. However, the safety and stability of applying DRL to safety-critical systems remain a primary concern and challenging problem. To address the problem, we propose the Phy-DRL: a novel physics-model regulated deep reinforcement learning framework. The Phy-DRL is novel in two architectural designs: a physics-model-regulated reward and residual control, which integrates physics-model-based control and data-driven control. The concurrent designs enable the Phy-DRL to mathematically provable safety and stability guarantees. Finally, the effectiveness of the Phy-DRL is validated by an inverted pendulum system. Additionally, the experimental results demonstrate that the Phy-DRL features remarkably accelerated training and enlarged reward. 

Nowadays, AI-based techniques, such as deep neural networks (DNNs), are widely deployed in autonomous systems for complex mission requirements (e.g., motion planning in robotics). However, DNNs-based controllers are typically very complex, and it is very hard to formally verify their correctness, potentially causing severe risks for safety-critical autonomous systems. In this paper, we propose a construction scheme for a so-called Safe-visor architecture to sandbox DNNs-based controllers. Particularly, we consider the construction under a stochastic game framework to provide a system-level safety guarantee which is robust to noises and disturbances. A supervisor is built to check the control inputs provided by a DNNs-based controller and decide whether to accept them. Meanwhile, a safety advisor is running in parallel to provide fallback control inputs in case the DNN-based controller is rejected. We demonstrate the proposed approaches on a quadrotor employing an unverified DNNs-based controller.