On Two-Sided Approximations of Reachable Sets of Control Systems with Geometric Constraints on the Controls

We consider a nonlinear control system in Euclidean space on a finite time interval with controls subject to geometric constraints. The question of constructing lower and upper (by inclusion) approximations of reachable sets of this system is studied. Under certain conditions, estimates are obtained...

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Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 313; no. Suppl 1; pp. S211 - S227
Main Authors Ushakov, V. N., Pershakov, M. V.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Moscow Pleiades Publishing 01.08.2021
Springer Nature B.V
Subjects
Approximation
Control systems
Euclidean geometry
Euclidean space
Geometric constraints
Mathematics
Mathematics and Statistics
Metric space
Nonlinear control
geometric constraints
approximation
control
differential inclusion
control system
reachable set
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Summary:We consider a nonlinear control system in Euclidean space on a finite time interval with controls subject to geometric constraints. The question of constructing lower and upper (by inclusion) approximations of reachable sets of this system is studied. Under certain conditions, estimates are obtained for the discrepancy (in the Hausdorff metric) between the lower and upper approximations of the reachable sets.
Bibliography:ObjectType-Article-1
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SourceType-Conference Papers & Proceedings-1
content type line 22
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543821030226