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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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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description 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.
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subjects Control systems
Differential equations
Euclidean geometry
Euclidean space
Funnels
Inclusions
Mathematics
Mathematics and Statistics
Metric space
Nonlinear control
Variable structure control
title Control Systems of Variable Structure. Attainability Sets and Integral Funnels
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