Optimal Hâˆ‍ Based Linear Quadratic Regulator Tracking Control for Discrete Time Takagi–Sugeno Fuzzy Systems With Preview Actions

Abstract

This paper investigates the optimal tracking control problem for discretetime Takagi–Sugeno (T–S) systems. The control signal has three components: preview control for the previewable reference signal, integral control for the tracking error, and the statefeedback control for the plant. The optimization objective is a quadratic form of the tracking error and the control signal. By using the augmentation technique, the tracking controller design problem is converted into a design problem of the statefeedback controllers for augmented T–S fuzzy systems. The quadratic optimization objective is equivalent to the twonorm (in fact, the square of the twonorm) of a controlled output. Assuming that the external inputs of the augmented systems are l2 bounded, the Hâˆ‍ performance index is employed to investigate and optimize the controller design. The controller gains can be obtained by solving a sequence of linear matrix inequalities (LMIs). An example on electromechanical system shows the efficacy of the proposed design method.