Linear quadratic optimal control via using dynamic compensator

Abstract

The linear-quadratic (LQ) optimal problem based on dynamic compensation is considered for a general quadratic performance index in this paper. First, it is shown that there exists a dynamic compensator with a proper dynamic order such that the closed- loop system is asymptotically stable and its associated Lyapunov equation has a symmetric positive-definite solution. Then, the quadratic performance index is derived to be a simple expression related to the symmetric positive-definite solution and the initial value of the closed-loop system. In order to solve the optimal control problem for the system, the proposed Lyapunov equation is transformed into a Bilinear Matrix Inequality (BMI) and a corresponding path-following algorithm to minimize the quadratic performance index is proposed in which an optimal dynamic compensator can be obtained. Finally, several numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed approach.