Optimal quadratic regulation for discrete-time switched linear systems: A numerical approach

This paper studies the discrete-time linear quadratic regulation problem for switched linear systems (DLQRS) based on dynamic programming approach. The unique contribution of this paper is the analytical characterizations of both the value function and the optimal control strategies for the DLQRS problem. Based on the particular structures of these analytical expressions, an efficient algorithm suitable for solving an arbitrary DLQRS problem is proposed. The algorithm is also tested through simulations on a number of second-order DLQRS problems. Simulation results indicate that the proposed algorithm can solve the second-order DLQRS problems with very low computational complexity. The theoretical analysis in this paper dramatically simplifies the computation, making an NP hard problem numerically tractable.