Fuzzy Control Of Nonlinear Systems Based On TS Model  Posted on:20101125  Degree:Doctor  Type:Dissertation  Country:China  Candidate:G Zhang  Full Text:PDF  GTID:1118360302469351  Subject:Applied Mathematics  Abstract/Summary:  PDF Full Text Request  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. In 1985, Takagi T and Sugeno M proposed the TakagiSugeno (TS) fuzzy model, which brings farresearching impact on fuzzy control theory and its application, and makes the stability analysis of fuzzy systems to a new theoretical height. Combining with the Lyapunov stability theory, robust control theory and HÃ¢Ë†Å¾control theory, using the Linear Matrix Inequality (LMI), this thesis discussed the stability and stabilization problems of fuzzy systems based on TS linear model and TS bilinear model in detail, respectively.The main research works in this thesis can be described as follows:1. By constructing new appropriate fuzzy Lyapunov function and considering the useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov function, the delaydependent stability criteria of openloop fuzzy systems with timevarying delay are derived. Then, based on parallel distributed compensation (PDC) scheme, the delaydependent stabilization conditions of the closedloop systems are derived and the corresponding state feedback controller can be obtained, respectively.2. Based on fuzzy Lyapunov function and fuzzy freeweighting matrices with timevarying delay, some new sufficient conditions for robust HÃ¢Ë†Å¾stabilization of uncertain continuoustime fuzzy system with timevarying delay are given. The fuzzy freeweighting matrices are introduced, the purpose of which is to relax the constraint of the derivatives of timedelay.3. In order to reduce the conservation of the common Lyapunov function,based on fuzzy Lyapunov function and PDC scheme, the HÃ¢Ë†Å¾stability analysis of fuzzy delay discretetime systems and robust HÃ¢Ë†Å¾stability analysis of uncertain fuzzy delay discretetime systems are studied, respectively. Introducing the relax matrix, the fuzzy controllers design is presented in the form of LMIs, respectively.4. Stability analysis and synthesis of continuoustime nonlinear systems based on the TS bilinear model are investigated. By using Lyapunov function and PDC scheme, some sufficient conditions for multiple inputs fuzzy bilinear systems to be robust HÃ¢Ë†Å¾stable are derived. Then, the delaydependent stability of fuzzy systems with timevarying delay both in state and input is discussed and an LMI based controller design method is obtained. Finally, based on the static outputfeedback controller, some sufficient conditions for the fuzzy bilinear systems to be stable are obtained in the form of LMIs.5. The stability of discretetime fuzzy bilinear systems based on the TS bilinear model is analyzed. By using Lyapunov function, some sufficient conditions for multiple inputs discretetime fuzzy systems to be stable are derived. Then, the problem of stability analysis and synthesis of fuzzy systems with timedelay both in state and input are discussed. Sufficient conditions are derived for stabilization and are formulated in the form of LMIs. Finally, based on the piecewise Lyapunov function and switching fuzzy model, considered the interactions among the fuzzy subsystems in each subregion, the relaxed stabilization conditions are obtained for the fuzzy bilinear systems.6. In the presence of the additive controller gain perturbations, the nonfragile guaranteed cost control problems for the continuoustime and discretetime fuzzy bilinear systems with timedelay in both state and input are considered, respectively. Based on the PDC approach, the nonfragile guaranteed cost state feedback controllers design is obtained, such that the closedloop systems are asymptotically stable and the closedloop performance is no more than a certain upper bound of a given quadratic cost function.7. The problem of decentralized robust control for a nonlinear interconnected system composed by TS bilinear models with interconnections is considered. Based on the Lyapunov stability analysis theory and decentralized control theory, some sufficient robust stabilization conditions are derived for the whole closedloop fuzzy interconnected systems.Finally,some concluding remarks are given, and the future research works are pointed out.
 Keywords/Search Tags:  TS linear model, TS bilinear model, Fuzzy system, Parallel distributed compensation(PDC), Fuzzy Lyapunov function, Robust control, Nonfragile guaranteed cost control, Linear matrix inequality(LMI), Decentralized control  PDF Full Text Request  Related items 
 
