Problem of constructing a step function fluctuating least around a given function

Abstract

It is well known that step functions are often used in regulation and optimal control. Nevertheless, to our knowledge, this problem has not been raised previously. Therefore, the problem of constructing a step function, least fluctuating around a given function (in the sense of integration), is the main point of this article. This is a multiextremal task. In particular, such problems mostly arise in the design.In this paper formulated a mathematical model of the problem. To solve the problem developed an effective method of shrinking neighborhoods. Moreover, for algorithm of the method was developed software.