Abstract

Optimal control of switched systems is challenging due to the discrete nature of the switching control input. The embedding-based approach is one of the most effective approaches for addressing such a challenge. It tries to compute the optimal switching input by solving a corresponding relaxed optimal control problem with only continuous inputs, and then projecting the relaxed solution back to obtain the optimal switching solution of the original problem. This paper presents a novel idea that views the embedding-based approach as a change of topology over the optimization space, resulting in a general procedure to construct a switched optimal control algorithm with guaranteed convergence to a local optimizer. Our result provides a unified topology-based framework for the analysis and design of various embedding-based algorithms in solving the switched optimal control problem and includes many existing methods as special cases. I.