Multi-Objective Control of Distributed Parameter Systems in the Case of Interval Uncertainty of the Plant Characteristics

Abstract

The previously developed technology of multi-objective optimization of deterministic systems with distributed parabolic parameters can be applied in typical situations with interval uncertainties of parametric characteristics of controlled plants. Minimax problems of mathematical programming are formed in accordance with a control strategy based on the principle of the best guaranteed result of a expanded set of arguments, which includes all permissible realizations of uncertain factors, in the case of estimating a given accuracy of approximation to a required finite system state in uniform metric. These problems are solved by an alternance method that uses the Chebyshev properties of desired extermals and fundamental laws of the problem domain. This paper also presents an example of multi-objective optimization of temperature modes of induction heating of metallic semifinished products before plastic deformation operations in technological complexes for pressure treatment of metal, which is of independent interest.