The problem of reconstructing an unknown disturbance in a system of ordinary differential equations of a special kind is investigated on the basis of the approach of the theory of dynamic inversion. A statement is considered in which the disturbance is reconstructed synchronously with the process from incomplete discrete information on a part of coordinates of the phase trajectory. A finite-step software-oriented solution algorithm based on the method of auxiliary closed-loop models is proposed, and its error is estimated. The novelty of the paper is that we consider the inverse problem for a partially observed system with a nonlinear with respect to disturbance equation describing the dynamics of the unmeasured coordinate.
Keywords: system of ordinary differential equations, nonlinearity with respect to disturbance, lack of information, dynamic reconstruction, controlled model
Received March 16, 2021
Revised April 20, 2021
Accepted April 26, 2021
Valeriy Lvovich Rozenberg, Cand. Sci. (Phys.-Math.), Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural State University of Railway Transport, Yekaterinburg, 620034 Russia, e-mail: rozen@imm.uran.ru
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Cite this article as: V.L. Rozenberg. On a problem of dynamic disturbance reconstruction in a nonlinear system of differential equations, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 2, pp. 197–207.
