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ON AN ALGORITHM OF DISTURBANCE RECONSTRUCTION FOR A NONLINEAR DIFFERENTIAL-ALGEBRAIC SYSTEM
- Authors: Maksimov V.I1, Larin E.T1
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Affiliations:
- N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of RAS
- Issue: Vol 61, No 11 (2025)
- Pages: 1510-1526
- Section: CONTROL THEORY
- URL: https://journals.rcsi.science/0374-0641/article/view/352959
- DOI: https://doi.org/10.7868/S3034503025110063
- ID: 352959
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Abstract
The problem of reconstructing an unknown disturbance in a nonlinear system consisting of a combination of differential and algebraic equations is considered. Two cases are discussed. In the first case, a disturbance enters the system linearly; while in the second one, nonlinearly. In the case of linearity, the problem has two specific features. First, it is assumed that only a part of phase coordinates of the system (namely, the coordinates described by the differential equation) is inaccurately measured at discrete times. Second, it is only known about the disturbance acting on the system that it is an element of the space of square integrable functions; i.e., it can be unbounded. These assumptions imply the impossibility of exact reconstruction. Taking into account this peculiarity, we construct a solving algorithm, which is stable with respect to informational noises and computational errors. This algorithm is based on a combination of elements of the theory of ill-posed problems and the extremal shift method well-known in the theory of positional differential games. A similar algorithm is designed for a general case when a disturbance enters the system nonlinearly.
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About the authors
V. I Maksimov
N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of RAS
Email: maksimov@imm.uran.ru
Yekaterinburg
E. T Larin
N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of RAS
Email: larin.gor@bk.ru
Yekaterinburg
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