Singular Optimal Linear Quadratic Regulator of Switched Systems

Abstract

In this paper, we will investigate the singular linear quadratic regulator (LQR) problem of switched linear system in finite time horizon. The proposed method is transforming into a switched LQR problem by adopting linear transformation. Next, we adopt an embedding transformation method to convert the switched LQR problem to a traditional optimal control problem, so the bang-bang-type solution of the embedded optimal control problem in finite time is the optimal solution to the switched LQR problem. The switching sequence of modes and the switching instants can be calculated by solving a closed-form optimal switching condition. The optimal state feedback control law is determined simultaneously. Then, by solving a sequence of Riccati equation, we find some conditions that ensure switched LQR problem can be convert to the singular LQR problem. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.