SOGARG: A Self-Organized Genetic Algorithm-based Rule generation Scheme for Fuzzy Controllers

Abstract—This paper presents a self-organized genetic algo-rithm-based rule generation (SOGARG) method for fuzzy logic controllers. It is a three-stage hierarchical scheme that does not re-quire any expert knowledge and input-output data. The first stage selects rules required to control the system in the vicinity of the set point. The second stage starts with the rules resulted from the first stage and extends its span of operation to the entire input space. Thus, the second stage ends up with a rulebase that can bring the system to its set point from almost all initial states of the input space. The third stage then refines the rulebase and reduces the number of rules in the rulebase. The first two stages use the same fitness function whose aim is only to acquire the controllability, but the last stage uses a different one, which attempts to optimize both the settling time and number of rules without compromising the controllability of the system. The mutation operations used in different stages are chosen to be different to make them consistent with the goals of different stages. The effectiveness of SOGARG is demonstrated using two control problems: the inverted pendulum and the truck back. For the inverted pendulum, rule sets contain only 16.6 rules on average, which is about 4.8 % of all possible rules and it takes about 35 steps to control the system over the entire input space with an average integral time absolute error (ITAE) of 0.1019. For the truck back, we get on average 23 (6.7%) rules, and for this the average time steps and the average ITAE are, respectively, 40 and 71.42. SOGARG is found to be not sensitive to the changes in the parameters of the genetic algorithms and to the changes in the system parameters. To demonstrate the superiority of our method, we compare our results with that of Lim et al., 1996 and Chan et al., 2000. Index Terms—Controllability, fuzzy controllers, genetic algo-rithm (GA), robustness, self-organizing. I