This article is cited in 5 papers

Optimality conditions of the maximum principle type in bilinear control problems

V. G. Antonik, V. A. Srochko

Irkutsk State University, Irkutsk, Russia

Abstract: The optimization of a bilinear functional related to a linear state system with a modular control constraint is considered. Exact formulas for the functional increment are used to obtain sufficient conditions for the optimality of extremal controls that supplement the maximum principle. These conditions are represented in the form of inequalities and equalities for one-variable functions on a time interval. The optimization of a quadratic functional with the help of a matrix conjugate function is reduced to the bilinear case.

Key words: linear state system, bilinear functional, sufficient optimality conditions.

UDC: 519.626

Received: 15.12.2015
Revised: 04.04.2016

DOI: 10.7868/S0044466916120024

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:12, 2023–2034

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