A simple weight based fuzzy logic controller rule base reduction method

This paper proposes a new rule base reduction method for Takagi-Sugeno type fuzzy logic controller. This method is cell state space based. First, the controller inputs are fuzzified and a generic rule base is built. This rule base includes all the possible combinations of input values. A search algorithm called Incremental Best Estimate Directed Search (IBEDS) is invoked to find the parameters in rule output functions. IBEDS starts with an initial training set. Each point inside the training set represents a currently best estimate control command for a cell center. Then another random FLC is trained in an iterative procedure by a Least Mean Square (LMS) algorithm. In each iteration, the cell state space based global and local performance of the trained FLC are evaluated, the training set is then updated based on the evaluation. When IBEDS converges, the final training set contains the maximal number of cells that a single FLC can control. At this stage, for each rule in the rule base, the firing strength or weight of the rule is calculated with every point from the training set. All the weights are added up to get a final Importance Index for that rule. A designer can cut off the rules with smallest importance indexes. A designer can cut as many rules as wanted according to the importance indexes. An FLC with reduced rule base is optimized by IBEDS again to achieve optimal performance. A 4D inverted pendulum is tested to justify the method. Each of the four inputs is fuzzified into 3 fuzzy values. A generic controller with 81 rules is built. After the optimization, the rule base is reduced to 40, 28, 17, and 5 respectively. The performances of the controllers with different rule bases are compared. It is shown that a controller with only 5 rules can perform comparably well with a controller of 81 rules.