Optimal switching for linear quadratic problem of switched systems in discrete time

The optimal switching problem is attracting plenty of attention. This problem can be considered as a special type of discrete optimization problem and is NP complete. In this paper, a class of optimal switching problem involving a family of linear subsystems and a quadratic cost functional is considered in discrete time, where only one subsystem is active at each time point. By deriving a precise lower bound expression and applying the branch and bound method, a computational method is developed for solving this discrete optimization problem. Numerical examples have been implemented to demonstrate the efficiency and effectiveness of the proposed method.