On one algorithm for reconstruction of an disturbance in a linear system of ordinary differential equations

• Autorzy: Blizorukova M. , Maksimov V.

Identyfikatory

DOI

10.24425/acs.2020.135851

• Języki publikacji: EN

Abstrakty

EN

The problem of reconstructing an unknown disturbance under measuring a part of phase coordinates of a system of linear differential equations is considered. Solving algorithm is designed. The algorithm is based on the combination of ideas from the theory of dynamical inversion and the theory of guaranteed control. The algorithm consists of two blocks: the block of dynamical reconstruction of unmeasured coordinates and the block of dynamical reconstruction of an input.

Słowa kluczowe

EN

dynamical reconstruction; guaranteed control; stable algorithm

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2020
• Tom: Vol. 30, No. 4
• Strony: 757--773
• Opis fizyczny: Bibliogr. 15 poz., wykr., wzory

Twórcy

autor

Blizorukova M.

• Krasovskii Institute of Mathematics and Mechanics of Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990 Russia

autor

Maksimov V.

• Krasovskii Institute of Mathematics and Mechanics of Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990 Russia

Bibliografia

• [1] H. T. Banks and K. Kunisch: Estimation Techniques for Distributed Parameter Systems, Boston: Birkhäuser, 1989.
• [2] Y. Bar-Shalom and X. R. Li: Estimation and Tracking: Principles, Techniques, and Software, Boston: Artech House, 1993.
• [3] N. N. Krasovskii and A. I. Subbotin: Game-Theoretical Control Problems, New York-Berlin: Springer Verlag, 1988.
• [4] A. Kuklin, V. Maksimov, and N. Nikulina: On reconstructing unknown characteristics of a nonlineas system of differential equations, Archives of Control Sciences, 23(2) (2015), 163–176.
• [5] L. Ljung and T. Söderström: Theory and Practice of Recursive Identification, Massachusetts: M. I. T. Press, 1983.
• [6] V. I. Maksimov: Dynamical Inverse Problems for Distributed Systems, Utrecht-Boston: VSP, 2002.
• [7] V. I. Maksimov: The tracking of the trajectory of a dynamical system, J. Appl. Math. Mech., 75 (2011), 667–674.
• [8] V. I. Maksimov: An algorithm for reconstructing controls in a uniform metric, J. Appl. Math. Mech., 77(2) (2013), 212–219.
• [9] V. I. Maksimov: Game control problem for a phase field equation, J. Optim. Theory and Appl (2016), JOTA-D-14-00400R1, DOI: 10.1007/s10957-015-0721-0.
• [10] V. I. Maksimov: Dynamic reconstruction of system disturbances using inaccurate discrete measurements of phase coordinates, J. Computer. Syst. Sc. Int., 57(3) (2018), 358–373.
• [11] V. I. Maksimov and F. Tröltzsch: Input reconstruction by feedback control for the Schlogl and Fitzhugh-Nagumo equations, Int. J. Appl. Math. Comput. Sci., 30(1) (2020), 5–22.
• [12] J. P. Norton: An Introduction to Identification, London: Academic Press, 1986.
• [13] Yu. S. Osipov and A. V. Kryazhimskii: Inverse Problems for Ordinary Differential Equations: Dynamical Solutions, London: Gordon and Breach, 1995.
• [14] Yu. S. Osipov, A. V. Kryazhimskii, and V. I. Maksimov: Methods of Dynamical Reconstruction of Inputs of Control systems, UrO RAN, Ekaterinburg (in Russian), 2011.
• [15] H. Unbehauen and G.P. Rao: Identification of Continuous Systems, Amsterdam: Elsevier, 1987.

Uwagi

The work is done within the framework of research of Ural Mathematical Center