Fuzzy adaptive approach to fuzzy controllers with spacial model

Abstract

In this paper, a fuzzy adaptive approach to fuzzy controllers designed with the spacial model is proposed. The complexity, which is defined as the size of the fuzzy rule base of the fuzzy controller, is significantly reduced based on the proposed approach. In order to reduce the number of fuzzy if–then rules, the multidimensional space of input variables (instead of the individual input variable) of fuzzy controllers is partitioned into fuzzy sets. However, this space partition method may degrade the performances of fuzzy controllers since the degree of freedom is decreased. To avoid the drawback of the (fixed) space-partitioned fuzzy controllers, a flexible spacial model design with fuzzy adaptive approach is introduced. Moreover, the fuzzy adaptive mechanism is designed to accelerate the convergence to the desired system output. The cascade decomposition of the fuzzy controllers designed with the flexible spacial model approach is presented to make these fuzzy controllers easy to implement. And the discussions on more general types of the membership functions for the flexible spacial fuzzy model and the stability of the system with the proposed fuzzy controller are provided. The simulation results are also included to show the effectiveness of the fuzzy controller by the flexible spacial model design approach. We will show that the complexity-reduced fuzzy controller with flexible spacial model and original fuzzy controller have similar performances and perform better than the fuzzy controller with simple fixed spacial fuzzy partition.