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.

Keywords:

step functions, calculus of variations, optimal control, pipelines, pumping stations, regulating tanks.