Evolving Optimal Fuzzy Logic Controllers by Genetic Algorithms

Abstract

The objective of this paper is to present an optimal design of Fuzzy Logic Controllers (FLCs) by Genetic Algorithms (GAs). As part of this objective, the design of input and output Membership Functions (mfs) of FLC is carried out simultaneously with input and output Scaling Factors (sfs). FLC since can be subjected to a range of set points, so the step size for mutation of alleles, and fitness function are adapted based upon Set Point Change (SPCs) commands, and besides, bounds of either input and output mfs or else of sfs are SPC-adapted; the latter two adaptations are demonstrated to be equivalent. Tuning is based upon maximization of a comprehensive fitness function constructed as inverse of a weighted-average of Integral Square Error (ISE), Peak Overshoot (Mp), Rise Time (tr) and Settling Time (ts), wherein weights for ISE and Mp are adapted. GA-evolved FLC (henceforth GAFLC) shows better closed-loop performance on linear and nonlinear stable and unstable systems as compared to a hand-designed FLC and a GA-designed PID (Proportional-Integral-Derivative Controller). This performance is almost fully preserved by GAFLC, under a wide range of SPCs, for linear systems (and the PID is demonstrated to share this property) and is better preserved by GAFLC than by PID for nonlinear systems. Some future directions are listed.