Control Systems of Variable Structure. Attainability Sets and Integral Funnels

We consider a nonlinear control system in a finite-dimensional Euclidean space and on a finite time interval. The system varies over some less time interval, and the differential equation describing the system is replaced with some other differential equation. As a result, a new control system appea...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-02, Vol.260 (6), p.820-832
Main Authors: Ushakov, V. N., Ukhobotov, V. I., Ushakov, A. V., Izmest’ev, I. V.
Format: Article
Language:English
Subjects:
Control systems
Differential equations
Euclidean geometry
Euclidean space
Funnels
Inclusions
Mathematics
Mathematics and Statistics
Metric space
Nonlinear control
Variable structure control
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Summary:We consider a nonlinear control system in a finite-dimensional Euclidean space and on a finite time interval. The system varies over some less time interval, and the differential equation describing the system is replaced with some other differential equation. As a result, a new control system appears on the initial time interval. We study how much the integral funnel of the system is changed under such a replacement. We obtain the upper estimate for the Hausdorff distance between the integral funnels of differential inclusions related to the initial and varied systems.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05730-1