Sliding Mode Preview Control for a Class of Continuous-Time Linear Systems

In this paper, the sliding mode preview control problem for a class of continuous-time linear systems is studied. Firstly, an extended error system consisting of the error equation and the state equation of the original system is constructed, and the tracking problem is transformed into the regulation problem. Secondly, a quadratic performance index function is introduced for the state variables of the extended error system, and the preview sliding surface is designed based on the existing conclusions of the optimal preview control. Thirdly, the sliding mode controller with preview effect for the extended error system is designed by using the reaching law method; then, the desired sliding mode preview controller of the original system can be obtained through the integral. The numerical simulation verifies the feasibility of the proposed method.