|dc.description.abstract||There are many physical systems which consist of multiple subsystems and are linked via a network of interconnections. These systems are called large-scale systems and they, and especially their inherent control design problems, have been considered by many fuzzy control papers. From the results of these researches, we know that the most important and difficult part of designing a fuzzy controller for large-scale systems is handling the nonlinear interconnections. Since each subsystem has several interconnections with the other subsystems, an entire nonlinear large-scale system contains a lot of interconnections. In general, if a nonlinear large-scale system is transformed into a Takagi-Sugeno (T-S) fuzzy system, one of two methods have been used to cope with the nonlinear interconnections before designing the fuzzy controller to stabilize the system. The first method is to set some specific bounded conditions in which the interconnections must satisfy. As a result, the nonlinear interconnections can be transformed into one set of linear functions. Then, the closed loop system can be solved by the Linear Matrix Inequality (LMI) method. Unfortunately, if the dynamics of the interconnections are not known in advance, then the interconnections’ bounded conditions must be checked in the simulation process. The second method is to linearize those nonlinear interconnections using the most popular ‘sector nonlinearity’ method or ‘local approximation in fuzzy partition spaces’ method. However, if the system consists of a large number of subsystems and each interconnection is transformed into a set of fuzzy rules, then the ‘rule-explosion’ problem may happen.
This dissertation proposed several novel methods to solve the above two problems. Firstly, regarding to the problem of bounding constraint of interconnections, we introduce the robustness and H-infinity concept into the control design in order to decrease the conservatism. With the aids of robustness and H-infinity controller design methods, the conservatism caused by the norm inequality may be overcome and the corresponding controllers are obtained easily. Secondly, we develop one novel control design process. In this process, the ‘sector nonlinearity’ or ‘local approximation in fuzzy partition spaces’ methods are used to transform the original system into a T-S fuzzy system, and a Parallel Distributed Compensation (PDC) type fuzzy controller is designed. However, it should be emphasized that, in this process, the ‘rule-explosion’ problem is avoided because of a special derivation which eliminates the fuzzy rules generated by the interconnections, after which the S-procedure is used to obtain the stabilization conditions.
In conclusion, the proposed fuzzy control design processes in this dissertation are especially useful when the number of subsystems in the large-scale system is large. This is the most important contribution of this dissertation. Finally, we provide several numerical simulations in this dissertation in order to show the applications of the present fuzzy controller design approach.