Computational Mathematics and Mathematical Physics

, Volume 46, Issue 11, pp 1882–1895 | Cite as

Real-time calculation of the current state estimates for a class of delay systems

  • R. Gabasov
  • F. M. Kirillova
  • P. V. Makevich


The linear optimal observation problem is examined for one type of nonstationary delay system with an uncertainty in the initial state. A fast implementation of the dual method is proposed for calculating estimates of the initial state. This implementation is based on the quasi-reduction of the fundamental matrix of solutions to the mathematical model of delay systems. It is shown that an iteration step of the dual method only requires that auxiliary systems of ordinary differential equations be integrated on small time intervals. An algorithm is described for the real-time calculation of current state estimates. The results are illustrated by the optimal observation problem for a third-order stationary delay system.


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


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Copyright information

© MAIK “Nauka/Interperiodica” 2006

Authors and Affiliations

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

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