Research of extreme systems: methods of search for extremums in the case of single-parameter object

DOI №______

Abstract

The article deals with extreme systems, which are a kind of adaptive systems. The ways of searching for an extremum, as exemplified by a one-parameter object, are analyzed. Two main ways of searching for an extremum are considered: based on increase in output and sensitivity (the behavior of the derivative). The emphasis is put on the most common methods for determining the increment of the output: the method of alternate steps (incremental extreme systems) and method of remembering the extremum. The general conclusions are drawn in that for the search of an extremum and its exact evaluation, the controlling influence must change so that it is possible to check the behavior of the output beyond the point of the possible extremum; the controlling influence appears to contain two components: one that corresponds to the extreme value, the second - a tentative one that serves to search for an extremum. This is particularly evident in the search method with a periodic search signal, which serves to determine the properties of the object, that is, to search for an extremum.

Keywords: extreme systems, object, design, optimization, control, methods, signal.

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