Differentical equations, dynamical systems and optimal control

Input reconstruction problem for a nonlinear system of differential equations: the case of incomplete measurements

V. L. Rozenberg<sup>ab

a</sup> Krasovskii Institute of Mathematics and Mechanics UB RAS, S. Kovalevskoi str. 16, 620108, Yekaterinburg, Russia
^b Ural State University of Railway Transport, Kolmogorova str. 66, 620034, Yekaterinburg, Russia

Abstract: The problem of reconstructing an unknown input in a system of ordinary differential equations of a special kind is investigated by means of the approach of the theory of dynamic inversion. The input action should be reconstructed synchronously with the process of incomplete discrete measuring of 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 study the inverse problem for a partially observed system with a nonlinear with respect to input equation describing the dynamics of the unmeasured coordinate.

Keywords: nonlinear system of ordinary differential equations, incomplete measurements, dynamic reconstruction, controlled model.

UDC: 517.977

MSC: 49K15

Received April 12, 2022, published November 25, 2024

Language: English

DOI: 10.33048/semi.2024.21.071