Robust Preview Control for a Class of Uncertain Discrete-Time Lipschitz Nonlinear Systems

Abstract

This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems. According to the preview control theory, an augmented error system including the tracking error and the known future information on the reference signal is constructed. To avoid static error, a discrete integrator is introduced. Using the linear matrix inequality (LMI) approach, a state feedback controller is developed to guarantee that the closed-loop system of the augmented error system is asymptotically stable with H∞ performance. Based on this, the robust preview tracking controller of the original system is obtained. Finally, two numerical examples are included to show the effectiveness of the proposed controller.

Simplified Thermal Model and Optimal Control for Chilled Water Pipe in Air‐Conditioning System

“…Considering the results, T-SII model can apply to other equipment and system with the different initial values, and ( R ). Expediently, the LMI toolbox of MATLAB is used to determine the gain matrix of preview controller [22], and three situations ( R =0; R =10; R =20) are discussed to obtain the optimal coefficient for this experiment. In this simulation, the based coefficient matrix of T-SII model is shown in (37), and the reference signal is the regulating variable of temperature, and it can be taken as a step signal:…”

Output feedback preview tracking control for time‐varying polytopic descriptor systems

“…then system (27) is robustly asymptotically stable, and the gain matrix can be obtained by K = LU −1 . The controller is given by…”

“…For example, in the nonlinear case, the problem of stability analysis and control design has been studied based on the differentiable mean value theorem. 26,27 The problems of preview control of Takagi-Sugeno fuzzy systems have been investigated in the works of Wang and Aida 28 and Choi et al 29 and the problem of an integrated fault-tolerant preview tracking control framework has been investigated based on reduced-order simultaneous state and fault estimation in the work of Han et al 30 Additionally, the problems of adaptive preview controller design for discrete-time systems with unknown piecewise constant coefficients have been investigated in the works of Wang et al, 31,32 respectively. Some achievements have been made in the field of preview control for descriptor systems, eg, the problems of linear time-invariant descriptor systems have been studied in other works.…”

“…In recent years, a great deal of attention has been devoted to the incorporation of other theories and problems. For example, in the nonlinear case, the problem of stability analysis and control design has been studied based on the differentiable mean value theorem . The problems of preview control of Takagi‐Sugeno fuzzy systems have been investigated in the works of Wang and Aida and Choi et al and the problem of an integrated fault‐tolerant preview tracking control framework has been investigated based on reduced‐order simultaneous state and fault estimation in the work of Han et al Additionally, the problems of adaptive preview controller design for discrete‐time systems with unknown piecewise constant coefficients have been investigated in the works of Wang et al, respectively.…”

Observer‐based preview repetitive control for uncertain discrete‐time systems

“…Its study began in the 1960s 13 . Compared with other control methods, the main advantages of PC theory consist of enhancing the transient response of the closed‐loop system and reducing energy consumption 14 . In the past few years, the PC theory has been extensively considered in many fields, such as singular systems, 15,16 time delay systems, 17 stochastic systems, 18,19 and multi‐agent systems, 20 and so on.…”