A Safety-Certified Policy Iteration Algorithm for Control of Constrained Nonlinear Systems

Abstract

This letter designs safe controllers with guaranteed performance for continuous-time systems under state constraints. While existing safe control frameworks mainly ignore the performance of the controller and existing optimal control frameworks ignore the safety of the controller, the presented approach brings the best of both worlds of safe control design and optimal control design together. To this end, a novel safe policy iteration algorithm is presented that iteratively finds an optimal controller while certifying the safety of the improved control policy at each iteration. To avoid solving a Hamilton-Jacobi Bellman (HJB) equality for finding the optimal control policy, which does not guarantee safety, an HJB inequality is solved that can be integrated with barrier certificate to verify the safety of the control policy. Sum-of-Squares program is employed to implement the presented policy iteration algorithm and thus iteratively find a safe control solution with guaranteed performance. A simulation example is provided to verify the effectiveness of the proposed approach.