(1) Belarussian State University, pr. Nezavisimosti 4, Minsk, 220080, Belarus;(2) 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.