Finite-Horizon Optimal Control of Discrete-Time Switched Linear Systems - Qixin Zhu (Mathematical Problems in Engineering, 2012)
Finite-horizon optimal control problems for discrete-time switched linear control systems are investigated in this paper. Two kinds of quadratic cost functions are considered. The weight matrices are different. One is subsystem dependent; the other is time dependent. For a switched linear control system, not only the control input but also the switching signals are control factors and are needed to be designed in order to minimize cost function. As a result, optimal design for switched linear control systems is more complicated than that of non-switched ones. By using the principle of dynamic programming, the optimal control laws including both the optimal switching signal and the optimal control inputs are obtained for the two problems. Two examples are given to verify the theory results in this paper.