Parametric Optimization of Systems with Distributed Parameters in Problems with Mixed Constraints on the Final States of the Object of Control

Abstract

A constructive technology of the solution of the parametrized problems of the programmed optimal control of systems with the distributed parameters under the conditions of different requirements for the permissible deviation of the resulting spatial distribution of the controlled value from the set magnitude in the uniform metric is proposed. The developed technique uses a special procedure of the one-criterion convolution of the considered constraints and the subsequent reduction to the typical form of the problems of mathematical programming on the extremum of a function of a finite number of variables with an infinite number of constraints (semi-infinite optimization problem), which is solved by the scheme of the previously developed alternance method. An example of optimization by the criteria of the speed and energy consumption of unsteady heat conduction processes with two different restrictions on the accuracy of approximation to the given temperature conditions, which is of independent interest, is given.