Iterative fuzzy modeling using membership functions of degree n and its application to a crane control

In this paper, a simplified fuzzy reasoning model using triangular membership function is extended to a model whose fuzzy sets of the premise part of the fuzzy reasoning rule is defined by membership functions of degree n. The output of this model is a piecewise function of degree n. The authors introduce two iterative approximation schemes to identify the unknown function using fuzzy model. One is an iterative learning algorithm by means of steepest gradient method and the other is the pattern search method which minimize an objective function. An example of application for stabilizing control of a container crane is given. It is shown that the approximate optimal control can be obtained by the simple iterative algorithm. [In Japanese.]