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Preview Control for Discrete-Time Polytopic Time-Varying Systems with Input Saturation

LI Li1,2, LU Yanrong3   

  1. 1. School of Information Management and Statistics, Hubei University of Economics, Wuhan 430205;
    2. Hubei Center for Data and Analysis, Hubei University of Economics, Wuhan 430205;
    3. College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050
  • Received:2021-08-22 Revised:2021-12-05 Online:2022-06-25 Published:2022-07-29

LI Li, LU Yanrong. Preview Control for Discrete-Time Polytopic Time-Varying Systems with Input Saturation[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(6): 1438-1453.

For a class of uncertain discrete-time systems with time-varying polytopic and input saturation, a control method of reference preview compensation is proposed to achieve preview tracking performance in this paper. First, an auxiliary variable related to the state variable is introduced to constructed the augmented error system including previewed information. This leads to the preview control problem of the original system is transformed into the H control problem of the augmented error system. Then, for the augmented error system, a sector condition handles saturation is proposed to deal with the input saturation and a state feedback with preview actions is presented. Based on Lyapunov method and LMI technique, the conditions of asymptotic stability of the closed-loop system and the design method of the preview controller are given. The preview controller's gain matrix is obtained by solving LMI. Finally, the effectiveness of the results in this paper is illustrated by numerical simulation examples.

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