Hybrid optimal control for linear discrete-time systems by simultaneous optimization approach of system states and mode distributions

In this paper, we study optimal control problems for linear discrete-time hybrid systems. We adopt an approach to prepare some candidates of mode distributions and minimize value functions at each time for the systems and performance indices to optimize system states and mode distributions simultaneously. We state a class of principles of hybrid optimality, which gives a theoretical base of the approach. We consider optimal control problems for averaged systems and averaged performance indices throughout mode distributions to solve the original control problems. Finally we present numerical examples and verify that we can obtain both optimal control performance and optimal candidate of mode distributions by the algorithm presented in this paper.