Backpropagation learning for a fuzzy controller with partitioned membership functions

A backpropagation learning method is developed for partitioned, triangular, fuzzy input membership functions to account for the coupled nature of the function parameters. Partitioned, triangular input membership functions are common in industrial fuzzy applications. The resulting algorithm is applied to a Mamdani fuzzy logic system with product-sum inference and weighted-average defuzzification. The algorithm is developed from the standard backpropagation method with the complete impact of each input parameter change included in the partial derivative expansion of the system. The algorithm is applied to tune the input parameters of a controller for a two-link, planar robot. The system response is demonstrated for a set of commands which create cross-coupling through both centrifugal and Coriolis forces.