Linear quadratic optimal control based on dynamic compensation

The linear-quadratic optimal problem based on dynamic compensation is considered for a general quadratic performance index in this paper. First a dynamic compensator with a proper dynamic order is given 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 an 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 algorithm