Reduction of the number of rules in fuzzy controllers using genetic algorithm

A procedure for designing a Mamdani fuzzy logic controller including rule base reduction is proposed. The rules are modelled with binary weights on which constraints are imposed in order to ensure consistency. A simple genetic algorithm is used for finding stabilising controllers that minimise the number of rules. The design procedure involves the rule base and the distribution of the fuzzy sets in the universes of discourses. As an example the control of the pole and cart system is studied. The optimisation procedure produced compact fuzzy controllers with five rules having relatively good robustness properties.