Structural optimization of fuzzy systems' rules base and aggregation models

The purpose of this paper is to propose a general method to simplify the structure of fuzzy controllers' rule base using integrated methodology for reducing the number of fuzzy rules based on modelling and simulation.

The paper considers the problem of developing effective methods and algorithms for optimization of fuzzy rules bases of Sugeno‐type fuzzy controllers that can be applied to control of dynamic objects, including objects with non‐stationary parameters. The proposed approach based on calculating the impact of each of the rule on the formation of control signals for different types of input signals provides optimization of a linguistic rules database by using exclusion mechanism for rules with negligible influence. The effectiveness of the proposed approach is investigated using a fuzzy PID controller for control of a non‐stationary object of second order.

In this paper, the authors argued that different aggregation models can be used for structural optimization of fuzzy controllers and not all the rules are actually required in the fuzzy controllers' rule base. Eliminating some of the rules does not necessarily lead to a significant change in the fuzzy controller's output. The proposed integrated approach based on combination of different kinds of reference input signals for fuzzy controllers modelling and simulation is able to provide guidelines to the users which rules are required and which can be eliminated. The results obtained from the case studies demonstrate that the proposed integrated approach is able to reduce the number of rules required and, at the same time, to have the desired values of quality control indices.

In order to demonstrate the feasibility of the proposed approach, only control object of second order with PID fuzzy controller of Sugeno‐type is chosen. Future studies can advance this research by applying the proposed approach in different types of fuzzy systems.

The proposed integrated approach is able to simplify the structural optimization methodology and make it possible to be implemented in real processes of the fuzzy controllers' design.

The value of the current paper is on the proposal of an integrated approach for rule reduction to enhance the practical use of modelling and simulation in a design of fuzzy controllers.