Study On Some Control Problems Of TS Fuzzy Systems  Posted on:20100217  Degree:Doctor  Type:Dissertation  Country:China  Candidate:J X Dong  Full Text:PDF  GTID:1228330371450204  Subject:Navigation, guidance and control  Abstract/Summary:  PDF Full Text Request  With the developments of the science, we have more requirements for control systems and the control systems are more complex. The controlled object or process often is nonlinear, subject to some random disturbances and uncertainties, so that its mathematical model, which can satisfy our demands, is not available. For the control system, the conventional control theory is not applicable. However, the fuzzy control techniques with a property of human language can overcome the difficulties. In particular, stability analysis and control synthesis of nonlinear systems described by TS fuzzy models appeal many researchers’interest and many important progresses have been achieved. Due to the inherent nonlinearities of TS fuzzy systems, it is still a very important task to exploit more effective conditions for stability analysis and control synthesis.Based on the previous work of other researchers, this thesis further studies some control problems of TS fuzzy systems, which are given as follows:By using the properties of fuzzy membership functions, a new LMI technique, which can introduce more LMI variables than the existing ones, is proposed. Further, by the new technique, the conditions with less conservatism are given for stability analysis and control synthesis for continuoustime TS fuzzy systems; By using the properties of the null space of system output matrix, a new LMIbased condition for designing H^ static output feedback controllers for discretetime TS fuzzy systems is given. In contrast to the existing approaches, the new one removes the constraint on the structure of Lyapunov matrices, then it can gives less conservative results; A new control scheme for TS fuzzy systems, i.e., switching PDC control scheme, is proposed for the first time. The corresponding LMIbased control design approaches are given. The proposed approaches can be reduced to the PDC controller design methods or switching linear controller design methods under some additional constraints, then they can give less conservative results; A new type of TS fuzzy models, which consist of local nonlinear subsystems, is constructed for a class of nonlinear systems with strong nonlinearities, and the corresponding conditions for designing controllers are given. The proposed approach can overcome the difficulty of designing controllers based on the conventional TS fuzzy models due to too many fuzzy rules in the model. It can reduce the computational burden and give less conservative results; A controller design method for singularly perturbed fuzzy systems, which can improve the upper bound of the singular perturbation parameter by designing controllers, is given. The proposed method overcomes the difficulty that the existing approaches cannot improve the upper bound of the singular perturbation parameter by designing controllers. Moreover, a new condition for designing modeindependent controllers for Markovian jump fuzzy systems is given. More slack variables are introduced in the proposed condition, then the proposed method is more flexible in the freedom and can given less conservative results than the existing ones.The considered main issues are given as follows:In Chapter 1, the background and the development of fuzzy control are summarized and analyzed.In Chapter 2, a new LMI technique, which can introduce more variables, is exploited, then an LMIbased method with a linear search for designing fuzzy controllers for continuoustime TS fuzzy systems is obtained. In contrast to the existing approaches, the new one is more flexible in the freedom due to more slack variables, therefore, it can give less conservative results. Numerical examples are further given for showing the effectiveness of the proposed approach. Moreover, by using the properties of the null space of output matrices, a parameterdependent slack variable with lowertriangular structure is introduced, then a new method for designing static output feedback controllers is obtained. In contrast to the existing approaches, the proposed method can remove the constraint on Lyapunov matrices and give less conservative results. Numerical examples validate the effectiveness of the proposed approachIn Chapter 3. by analyzing the properties of fuzzy systems, a new control scheme, i.e., switching PDC control scheme, is proposed for the first time. LMIbased conditions for designing switching PDC controllers are given respectively for continuous and discretetime TS fuzzy systems. The existing PDC controller design methods or switching linear controller design methods can be considered as a special case of the new control scheme. Therefore, the proposed method can give less conservative results than the existing ones. Numerical examples are given to show the effectiveness of the proposed approaches.In Chapter 4, fuzzy controller design problems of a class of nonlinear systems with complex nonlinearities are considered. The TS fuzzy models of the class of nonlinear systems are of very many fuzzy rules, so that the methods for designing controller have heavy computational burden or cannot get a feasible solution. Moreover, the obtained controllers are not convenient for implementing in engineering. In order to overcome the difficulty, a new type of TS fuzzy models with local nonlinear subsystems are proposed and the corresponding control synthesis techniques are given. In contrast to the existing approaches, the proposed one can obtain a fuzzy controller with less fuzzy rules and has less computational burden. In particular, some important properties of nonlinear systems can be reserved due to the use of the nonlinear subsystems, then it also can give less conservative results. The effectiveness of the proposed method is validated by numerical examples.In Chapter 5, the problems of the controller design, and the estimation of the upper bound of singular perturbation parameter of singularly perturbed fuzzy systems are considered. A controller design method with improving the upper bound of the singular perturbation parameter is given for the first time for continuoustime singularly perturbed fuzzy systems. Moreover, two LMIbased conditions for designing Hx controllers only by slow state information for discretetime singularly perturbed fuzzy systems are proposed, where one of them can improve the upper of singular perturbation parameter by designing controllers. Both of them remove the constraint on Riccati equation or inequality approaches, where the systems have to satisfy the regularity. The effectiveness of the proposed methods are validated by numerical examples.In Chapter 6, based on stochastic Lyapunov functions and by introducing slack variables for separating the system matrix and Lyapunov matrix, an LMIbased condition for designing modeindependent controllers is given for Markovian jump fuzzy systems. In contrast to the existing approach, the proposed method is of more LMI variables, then can give less conservative results. Numerical examples further show the effectiveness of the proposed method.Finally, the results of the dissertation are summarized and further research topics are pointed out.  Keywords/Search Tags:  TS fuzzy systems, nonlinear systems, state feedback control, static output feedback control, dynamic output feedback control, H_oo control, H2 control, switching control, singularly perturbed systems, Markovian jump systems  PDF Full Text Request  Related items 
 
