Nested design of fuzzy controllers with partial fuzzy rule base

Abstract

In this paper, a systematic nested design approach with a partial fuzzy if–then rule base is proposed to reduce the complexity of the fuzzy controllers. In the design procedure, the fuzzy controller is first constructed with a basic fuzzy rule base. When the fuzzy rule base is not sufficient to provide the performance that meets the requirement of the fuzzy control system, the fuzzy rule base contains some unsatisfactory fuzzy rules and needs to be adjusted. After the unsatisfactory fuzzy rules are identified, the fuzzy region controlled by each unsatisfactory fuzzy rule is further partitioned into sub-regions. Based on the nested design procedure, the partial fuzzy rule base of the fuzzy controller is modified by replacing each unsatisfactory fuzzy rule with new fuzzy rules for the corresponding sub-regions. Each fuzzy region of the input space can be partitioned independently into fuzzy sub-regions to avoid generating the redundant rules. The parameters in the fuzzy mechanism are tuned by minimizing a cost function. Simulations are carried out to show the effectiveness of the fuzzy controllers with nested fuzzy if–then rules.