An Efficient Dynamic Optimization Algorithm for Path-Constrained Switched Systems

Dynamic optimization is one of the model-based adaptive reinforcement learning methods, which has been widely used in industrial systems with switching mechanisms. This article presents an efficient dynamic optimization strategy to locate an optimal input and switch times for switched systems with guaranteed satisfaction for path constraints during the whole time period. In this article, we propose a single-level algorithm where, at each iteration, gradients of the objective function with respect to switch times and the system input are evaluated by solving adjoint systems and sensitivity equations, respectively. Then the optimization of the input is performed at the same iteration with that of the switch time vector, which greatly reduces the number of nonlinear programs (NLPs) and computational burden compared with multistage algorithms. The feasibility of the optimal solution is guaranteed by adapting a new policy iteration method proposed to switched systems. It is proven that the proposed algorithm terminates finitely, and converges to a solution which satisfies the Karush-Kuhn-Tucker (KKT) conditions to specified tolerances. Numerical case studies are provided to illustrate that the proposed algorithm has less expensive computational time than the bi-level algorithm.