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

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Abstract

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.

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References

  1. N. N. Krasovskii, Theory of Motion Control (Nauka, Moscow, 1968) [in Russian].

    Google Scholar 

  2. R. Gabasov and F. M. Kirillova, “Allied Control, Observation, and Identification Problems” Dokl. Akad. Nauk Belarusi 34(9), 777–780 (1990).

    MATH  MathSciNet  Google Scholar 

  3. R. Gabasov, N. M. Dmitruk, and F. M. Kirillova, “Optimal Observation of Nonstationary Dynamical Systems,” Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 2, 35–46 (2002) [J. Comput. Syst. Sci. Int., 41, 195–206 (2002)].

  4. R. Gabasov, N. M. Dmitruk, and F. M. Kirillova, “Optimal Control of Multidimensional Systems Based on Inaccurate Measurements of Output Signals,” in Trudy Instituta Matematiki i Mekhaniki, Ural. Otd. Ross. Akad. Nauk (Yekaterinburg, 2004), Vol. 10, No. 2, 35–57 [in Russian].

    Google Scholar 

  5. R. Gabasov, F. M. Kirillova, and O. P. Yarmosh, “Optimal Control of Systems Involving Delay,” Dokl. NAN Belarusi 49(6), 36–42 (2005).

    MathSciNet  Google Scholar 

  6. R. Gabasov, F. M. Kirillova, and A. I. Tyatyushkin, Constructive Optimization Methods, Part 1: Linear Problems (Universitetskoe, Minsk, 1984) [in Russian].

    Google Scholar 

  7. R. Gabasov, F. M. Kirillova, and S. V. Prischepova, “Optimal Feedback Control,” in Lecture Notes in Control and Information Science, Ed. by M. Thoma, (Springer, Berlin, 1995), Vol. 207.

    Google Scholar 

  8. J. K. Hale, Theory of Functional Differential Equations (Springer, New York, 1977; Mir, Moscow, 1984).

    MATH  Google Scholar 

  9. A. Manitius, “Feedback Controllers for a Wind Tunnel Model Involving a Delay: Analytical Design and Numerical Simulation,” IEEE Trans. Autom. Control 29(12), 1058–1068 (1984).

    Article  MathSciNet  Google Scholar 

  10. A. Manitius and H. Tran, “Numerical Simulation of a Nonlinear Feedback Controller for a Wind Tunnel Model Involving a Time Delay,” Optimal Control Appl. Meth. 7, 19–39 (1986).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Belarussian State University, pr. Skoriny 4, Minsk, 220080, Belarus

    R. Gabasov & P. V. Makevich

  2. Institute of Mathematics, Belarussian Academy of Sciences, ul. Surganova 11, Minsk, 220072, Belarus

    F. M. Kirillova

Authors
  1. R. Gabasov
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  2. F. M. Kirillova
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  3. P. V. Makevich
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Original Russian Text © R. Gabasov, F.M. Kirillova, P.V. Makevich, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 11, pp. 1972–1986.

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Gabasov, R., Kirillova, F.M. & Makevich, P.V. Real-time calculation of the current state estimates for a class of delay systems. Comput. Math. and Math. Phys. 46, 1882–1895 (2006). https://doi.org/10.1134/S0965542506110054

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  • DOI: https://doi.org/10.1134/S0965542506110054

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