Based On The Polynomial Fuzzy Model Of Robust Guaranteed Cost Control Of A Class Of Linear System And Network Control

In recent years, the research on the nonlinear systems has received increasing attention. In1985, the T-S fuzzy model proposed by Takagi and Sugeno guides a new path to solve the nonlinear systems control problems. Recently, T-S fuzzy model has been extended to polynomial fuzzy model, which represent nonlinear systems more effectively. In addition, with the trend of networked industrial systems, the communication network is introduced to the closed system. However, despite the advantages and potentials, communication network in the control loops arouse some new issues, which imposes a challenge to system analysis and design. In this paper, based on the Lyapunov stability theory, PDC principle and sum-of-squares (SOS) approach, guaranteed cost control and robust guaranteed cost control and networked control for nonlinear time-delay system based on polynomial fuzzy model are studied, which provides new results and new ideas in the fields of nonlinear system control and networked control.The main research works of this paper are as follows:(1) For a class of continuous nonlinear time-delay systems, using the time-delay polynomial fuzzy modeling. State-dependent Lyapunov-Kraovskii functional and PDC principle are utilized. By minimizing the upper bound of a given performance function, the guaranteed cost control design conditions are given and guaranteed cost controller is also designed. Take into account the uncertainty in modeling, the guaranteed cost control with norm bounded uncertainties is considered. With the wide application of computer systems analysis and control, discrete system is indispensable. Discrete nonlinear time-delay systems modeled as discrete time-delay polynomial fuzzy control system, the guaranteed control and robust guaranteed cost control for discrete time-delay polynomial fuzzy system are studied. The results corresponding to the continuous case are obtained. In addition, all the results in this paper are in terms of SOS, which can be solved efficiently via the recent developed MATLAB toolbox SOSTOOLS. Design examples are provided to illustrate the validity of the design approach.(2) Based on polynomial fuzzy model of the nonlinear NCS, the stabilization problem and H∞control are investigated. First, the polynomial fuzzy model is adopted for representing nonlinear NCS. Then, for the NCS with network-induced time delays and packet losses, applying polynomial Lyapunov-Kraovskii functional and by making use of novel techniques for time-delay systems, a fuzzy controller of networked control system is designed to ensure the closed-loop NCS is asymptotically stable and with a H∞performance. In addition, network-induced delay τk mentioned in this paper needs not to be restricted within one sampling period. And the result is applied to mass-spring system. Simulation examples demonstrate the effectiveness of the proposed method.