The Problem of the Optimal Strategy of Minimax Control by Objects with Distributed Parameters

Abstract

The problem of minimax control synthesis for objects that are described by a two-dimensional heat conduction equation of parabolic type is solved. It is assumed that the control object functions under uncertainty conditions, and the perturbations acting on the object belong to some given hyperelipsoid. The problem of constructing a regulator in the state of an object for cases of point and mobile limit control is considered in accordance with the integral-quadratic quality criterion. In the work, for the first time, a minimax approach was used to control the objects described by the two-dimensional parabolic type thermal conductivity equation; the theoretical positions of synthesis of minimax regulators for cases of lumped boundary (point) and moving regulators are considered; algorithmic software is developed that allows to simulate the dynamics of the constructed minimax-regulators and to investigate the corresponding transients.