Controller Design For Nonlinear Systems Based On Polynomial Fuzzy Model

By using the fuzzy membership function,polynomial fuzzy model can approximate the actual complex nonlinear system with arbitrary precision,which plays an important role in the study of the nonlinear system.Using sum of squares(SOS)method and Lyapunov stability theorem,the stability analysis and controller synthesis problems for polynomial fuzzy systems have been investigated by many scholars.However,the existing results about polynomial fuzzy systems are based on an assumption that the input matrix Bl(x)has at least one zero row,which may limit the application of the results.Therefore,in this thesis,we will remove the above-mentioned restriction on input matrix.This thesis will design a dynamic output feedback H? controller for discrete polynomial fuzzy system.Meanwhile,the problem of designing a fault-tolerant controller for the continuous polynomial fuzzy system whose input matrix Bl(x)has no zero row is also investigated.The main contents of this thesis are as follows:In Chapter 3,the problem of designing a dynamic output feedback H? controller for discrete polynomial fuzzy system is considered.By designing an H? controller,the influence of the disturbance on the system can be restrained.Using the system output as feedback signal,the theoretical results obtained in this thesis can be widely applied to the case in which system state cannot be measured.Based on the characteristic of the membership function,system space is accordingly divided,and the switching Lyapunov function,S-procedure and some slack matrices are adopted into the stability analysis so as to obtain less conservative conditions.Meanwhile,an assumption is made on the input matrix to deal with the nonlinear terms appeared in the design conditions.A dynamic output feedback H?controller is designed and simulation results prove the effectiveness of the proposed method.In Chapter 4,the state feedback controller design problem is investigated for the continuous polynomial fuzzy system,whose input matrix Bl(x)has no zero row.In order to gain less conservative conditions,a Lyapunov function which can rely on any state of the system is adopted for the stability analysis.A novel SOS optimization approach is given to deal with the index transformed by nonlinear terms so as to get its zero optimal value.If we cannot get its zero optimal value,according to Holder's inequality,a discriminant condition concerning with the nonlinear terms is given to guarantee the stability of the closed-loop system.The inverted pendulum nonlinear system is adopted in the simulation part and the simulation results show the effectiveness of the proposed method.In Chapter 5,the fault-tolerant control problem is considered for continuous polynomial fuzzy system with actuator fault.Based on the passive fault-tolerant method,a fault-tolerant controller is designed for continuous polynomial fuzzy system whose input matrix Bl(x)has no zero row.Meanwhile,the boundary information of membership function,which represents nonlinear characteristic of system,is adopted into the stability analysis to make the results less conservative.Simulation results show the effectiveness of the proposed method.Finally,the thesis of the dissertation are summarized and further research topics are pointed out.