Geodesic
Real-time calculation of current optimal feedbacks for a delay system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1744-1757

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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. 
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     title = {Real-time calculation of current optimal feedbacks for a~delay system},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a3/}
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R. Gabasov; F. M. Kirillova; O. P. Yarmosh. Real-time calculation of current optimal feedbacks for a delay system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1744-1757. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a3/