Evolutionary calibration of fractional fuzzy controllers

摘要

Fuzzy controllers (FCs) that are based on integer schemes have demonstrated their performance in an extensive variety of applications. However, several dynamic systems can be more accurately controlled by fractional controllers yielding an increased interest in generalizing the design of FCs with fractional operators. In the design stage of fractional FCs, the parameter calibration process is transformed into a multidimensional optimization problem where fractional orders, as well as the controller parameters of the fuzzy system, are considered as decision variables. Under this approach, the complexity of the optimization problem tends to produce multimodal error surfaces for which their respective cost functions are significantly difficult to minimize. Several algorithms based on evolutionary computation principles have been successfully applied to identify the optimal parameters of fractional FCs. However, most of them still exhibit serious limitation since they frequently obtain sub-optimal solutions after an improper equilibrium between exploitation and exploration in their search strategies. This paper presents an algorithm for the optimal parameter calibration of fractional FCs. In order to determine the best parameters, the proposed method uses a new evolutionary method called Social Spider Optimization (SSO), which is inspired on the emulation of the collaborative behavior of social-spiders. In SSO, solutions imitate a set of spiders, which cooperate to each other by following the natural laws of a cooperative colony. Unlike most of the existing evolutionary algorithms, the method explicitly evades the concentration of individuals in the best positions, avoiding critical flaws such as the premature convergence to sub-optimal solutions and the limited balance of exploration-exploitation. Numerical simulations have been conducted on several plants to show the effectiveness of the proposed scheme.