This article is cited in 1 paper

Real-time calculation of current optimal feedbacks for a delay system

R. Gabasov^a, F. M. Kirillova^b, O. P. Yarmosh<sup>a

a</sup> Belarussian State University, pr. Nezavisimosti 4, Minsk, 220080, Belarus
^b Institute of Mathematics, Belarussian Academy of Sciences, ul. Surganova 11, Minsk, 220072, Belarus

Abstract: A linear optimal control problem for a nonstationary system with a single delay state variable is examined. A fast implementation of the dual method is proposed in which a key role is played by a quasi-reduction of the fundamental matrices of solutions to the homogeneous part of the delay models under analysis. As a result, an iteration step of the dual method involves only the integration of auxiliary systems of ordinary differential equations over short time intervals. A real-time algorithm is described for calculating optimal feedback controls. The results are illustrated by the optimal control problem for a second-order stationary system with a fixed delay.

Key words: delay control systems, quasi-reduction of the fundamental matrix of solutions, fast implementation of the dual method, real-time optimal control.

UDC: 519.626.2

Received: 05.10.2005
Revised: 02.05.2006

 English version: Computational Mathematics and Mathematical Physics, 2006, 46:10, 1660–1673

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