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Computational Mathematics and Mathematical Physics

, Volume 46, Issue 10, pp 1660–1673 | Cite as

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

  • R. Gabasov
  • F. M. Kirillova
  • O. P. Yarmosh
Article

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.

Keywords

delay control systems quasi-reduction of the fundamental matrix of solutions fast implementation of the dual method real-time optimal control 

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Copyright information

© MAIK “Nauka/Interperiodica” 2006

Authors and Affiliations

  • R. Gabasov
    • 1
  • F. M. Kirillova
    • 2
  • O. P. Yarmosh
    • 2
  1. 1.Belarussian State UniversityMinskBelarus
  2. 2.Institute of MathematicsBelarussian Academy of SciencesMinskBelarus

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