Safe Controller Synthesis for Nonlinear Systems via Reinforcement Learning and PAC Approximation

Controller synthesis for nonlinear systems is an important research issue. Deep Neural Network (DNN) control policies obtained through reinforcement learning (RL), though exhibiting good performance in simulations, cannot be applied to safety-critical systems for lack of formal guarantee. To address this, this paper considers fully utilizing the advantages of RL for complex control tasks to obtain a well-performing DNN controller. Then, using PAC (Probably Approximately Correct) techniques, a polynomial surrogate controller with probabilistically controllable approximation error is obtained. Finally, the safety of the control system under the designed polynomial controller is verified using barrier certificate generation. Experiments demonstrate the effectiveness of our method in generating controllers with safety guarantees for systems with high dimensions and degrees.