On Controller Design And Application Problems For T-S Fuzzy Systems

As an active research field, the nonlinear system theory makes a rapid progress recently, which plays an important role in control fields. However, nonlinear systems can not be described with given functions precisely in many practical cases. Fuzzy system theory is successfully applied to many control problems because it does not need to accurate mathematical models of the system and can cooperate with human experts’ knowledge. Recent years have witnessed rapidly growing of fuzzy systems in theory and engineering applications. An advantage of a T-S fuzzy model is that, when it is applied to the system analysis and controller design, one can first represent a nonlinear system as a fuzzy model, and then study the problems of stability and controller design by using a systematic approach.When uncertainties and time delays always appear in a T-S fuzzy system, they may affect the system performance seriously, and even make the system unstable. Hence by using Lyapunov stability theory and linear matrix inequality (LMI) technique, this dissertation investigates stability analysis and synthesis problems of T-S fuzzy system and the applications to the network and chaotic system. The main contributions are listed as the following:For T-S fuzzy systems, H∞control problem is considered. A more concise and integral sufficient condition of system stability and and controller existence is proposed, which overcomes such a drawback that the interactions among the fuzzy subsystems are not considered. And it collects the subsystem interactions in a matrix, and is in the terms of linear matrix inequalities (LMI). The simulation example shows the effectiveness of the proposed method.In real word control problems, the system states may not be completely accessible. Based on the LMI technique, the problem of the dynamic output feedback control for uncertain T-S fuzzy system is concerned. A dynamic output feedback controller is designed so that the resulted closed-loop systems are asymptotically stable. The solution of the controller is transformed into the solvability of convex linear matrix inequalities. Therefore, the parameter of the controller could be solved directly via the LMI toolbox. The perfect performance of the dynamic output feedback controller is demonstrated by numerical examples.The fuzzy multi-objective control problem is investigated for a class of uncertain nonlinear system based on T-S fuzzy model. By constructing dynamic output feedback controller, sufficient conditions are presented in terms of LMI for given performance index and fuzzy control law, such that the closed-loop system is quadratically stable. The resulting closed-loop system satisfies the domain pole placement requirement and H∞disturbance attenuation. A numerical simulation example is presented to illustrate the effectiveness of the proposed design method.Delay-dependent stability analysis and synthesis of continuous time delay T-S fuzzy systems are thoroughly studied. By constructing Lyapunov-Krasovksii functions that take more consideration of interrelationship of various factors in system state functions, a new delay-dependent stability criterion via LMI approach is proposed. The delay-dependent condition has lower conservation and relaxes the restriction to time delays of the control systems. The corresponding numerical simulation results demonstrate the effectiveness of the proposed schemes.The network congestion has become an important problem, which restricts the development and application of networks. Active queue management (AQM) is a kind of congestion control mechanism based on router. Nowadays AQM is extensively studied due to good effect for constraining congestion. TCP network is a complex large system with respect to the nature of nonlinearity and uncertainty, which requires a kind of more robust AQM algorithm in order to obtain better congestion control effect. T-S fuzzy model can suitably representate a nonlinear system, and a fuzzy observer-based T-S fuzzy controller is designed. A T-S fuzzy model is built for the nonlinear TCP/IP network congestion control system. The performance of network congestion control system is improved by choosing appropriate fuzzy rules and membership functions, and the stability of the system is rigorously theoretic proved. Simulation results in different scenarios demonstrate that the proposed controllers have good stability and robustness with respect to the uncertainties of the number of active TCP sessions, link capacity and the round-trip time (RTT).Chaos is a kind of special complicated nonlinear systems, which is ubiquitous in nature. Because such chaotic systems progress certain features, such as high randomicity and hyper sensitivity to initial conditions, the application of chaos can be especially found in secure communications, signal progressing and image progressing etc. Chaos synchronization has become the key technique in secure communications. The complete synchronization and generalized projective synchronization of chaotic systems are discussed in this dissertation. First, the fuzzy sliding mode controller is given for a class of chaotic systems based on T-S fuzzy system. It can guarantee asymptotical synchronization of both drive and response systems. Then the generalized projective synchronization problem of delay chaotic systems is studied. A new fuzzy state observer is designed in terms of LMI. According to the Lyapunov stability theory, it is verified that the proposed scheme is feasible and globally stable. Finally, the corresponding numerical simulation results demonstrate the effectiveness of the proposed schemes.Lastly, the summary of the whole dissertation is given and the research directions in future are put forward.