Optimal Tracking Control for Uncertain Singularly Perturbed Systems

Abstract

In this paper, the problem of tracking control for uncertain singularly perturbed systems is studied. Firstly, the uncertain singularly perturbed system and the uncertain external system are combined to form an augmented system, and the optimal tracking problem is transformed into a new standard linear quadratic optimization problem. Then, based on the minimum principle, the minimum value of quadratic performance index and the tracking optimal controller of the system are obtained. For the controller with a feasible approximate solution of the generalized Riccati equation, the design method of the controller can be obtained in the form of linear matrix inequality (LMI). Finally, a numerical example is given to demonstrate the viability and rightness of the proposed conclusion.