Analysis And Design Of Nonlinear System Based On T-S Fuzzy Bilinear Models

Classical control theory has great effect on those accurate systems, but the effect on complex systems and the ones that can not be described exactly are not satisfactory. Compared with classical control systems, fuzzy control systems have the following two unmatched advantages. First, it can be easy to realize effectively human control strategies and experience in many applications. Second, it can achieve better control performance in the absence of the accurate mathematic model for the controlled system. For this reason, the fuzzy control theory can be used to solve above control problem. In1985, Takagi T and Sugeno M proposed a novel fuzzy ratiocination model, called Takagi-Sugeno (T-S) fuzzy model, which is applied widely to the identification,(wave) filtering and control of nonlinear dynamical systems now. It brings far-researching impact on fuzzy control theory and application. As a special kind of nonlinear system, bilinear system is simpler than common nonlinear system, and has better approximation to a described object than a linear one, there have been many results about the research for the bilinear system. In2007, scholars Li T H S and Tsai S H proposed the T-S fuzzy bilinear model which was utilized into a class of uncertain discrete systems, researched the robust H∞stability problem of fuzzy systems. This achievement makes the method based on T-S fuzzy bilinear model an important topic in control theory community.Combining with the Lyapunov stability theory, robust control theory, H∞control theory and adaptive control theory, using the Linear Matrix Inequality (LMI), this thesis discusses the stability, modeling and controller designing problems of fuzzy systems based on T-S bilinear fuzzy model, and get some new achievements.The main contributions included in this thesis can be summarized as follows:Firstly, a novel model is presented based on bilinear T-S model for a class of discrete-time nonlinear systems with multiple inputs. The stability conditions of the overall fuzzy control system are formulated by linear matrix inequalities (LMI) and the gain of controller is obtained by solving a set of linear matrix inequalities (LMI). Finally, the validity and applicability of the proposed schemes are demonstrated by a numerical simulation.Secondly, for the tracking control problem of the bilinear T-S systems with multiple inputs, the parallel distributed compensation (PDC) method is utilized to design a fuzzy controller. The sufficient conditions are derived to guarantee the stability of the overall fuzzy control system with multiple inputs. The simulation results illustrate the validity of the proposed schemes.At last, a new design scheme of stable fuzzy control for a class of nonlinear systems is proposed. The T-S fuzzy bilinear model is employed to represent the systems. First, the parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error caused by fuzzy modeling and the sufficient conditions with respect to decay rate a are derived by linear matrix inequalities (LMI). Then the error caused by fuzzy modeling is considered and the method of adaptive control is used to reduce the effect of the modeling error, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. Finally, the validity, applicability and superiority of the proposed schemes are demonstrated by a simulation example.