Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111256
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dc.contributor.authorGusev, M. I.en
dc.date.accessioned2022-05-12T08:15:26Z-
dc.date.available2022-05-12T08:15:26Z-
dc.date.issued2020-
dc.identifier.citationGusev M. I. Asymptotic Behavior of Small-Time Reachable Sets of Nonlinear Systems with Isoperimetric Constraints / M. I. Gusev // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2020. — Vol. 26. — Iss. 1. — P. 89-101.en
dc.identifier.issn0134-4889-
dc.identifier.otherAll Open Access, Bronze3
dc.identifier.urihttp://hdl.handle.net/10995/111256-
dc.description.abstractWe study the problem of an approximate description of reachable sets over small time intervals for affinecontrol systems with isoperimetric control constraints. An isoperimetric constraint is understood as an integral constraint of inequality type with the integrand depending on the control parameters and state variables of the system. Previously, a similar problem was considered under the assumption that the integrand depends only on the control parameters and is a positive definite quadratic form in these parameters. In this case, it was shown that, under certain conditions imposed on the controllability Gramian of the linearized system, the reachable set is convex and asymptotically close in shape to an ellipsoid in the state space for a sufficiently small length of the time interval. This ellipsoid is the reachable set of the system linearized along the trajectory corresponding to the null control. In this paper, it is proved that, under a slight strengthening of the conditions imposed on the controllability Gramian, this result remains valid if the integrand defining the isoperimetric constraints has the form of the sum of a positive definite quadratic form in the control parameters and a nonnegative function of the state variables. This asymptotic representation holds, in particular, for a fairly wide class of second-order systems affine in the control under the condition that the linearized system is completely controllable. The proof is based on the results of the theory of strongly convex sets and functions. © 2020 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.en
dc.format.mimetypeapplication/pdfen
dc.language.isoruen
dc.publisherKrasovskii Institute of Mathematics and Mechanicsen1
dc.publisherKrasovskii Institute of Mathematics and Mechanics UB RASen
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceTr. Inst. Mat. Meh. UrO RAN2
dc.sourceTrudy Instituta Matematiki i Mekhaniki UrO RANen
dc.subjectASYMPTOTICSen
dc.subjectCONTROL SYSTEMen
dc.subjectCONTROLLABILITY GRAMIANen
dc.subjectISOPERIMETRIC CONSTRAINTSen
dc.subjectREACHABLE SETen
dc.titleAsymptotic Behavior of Small-Time Reachable Sets of Nonlinear Systems with Isoperimetric Constraintsen
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/publishedVersionen
dc.identifier.scopus85090541548-
local.contributor.employeeGusev, M.I., Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108, Russian Federation, Ural Federal University, Yekaterinburg, 620083, Russian Federationen
local.description.firstpage89-
local.description.lastpage101-
local.issue1-
local.volume26-
local.contributor.departmentKrasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108, Russian Federation; Ural Federal University, Yekaterinburg, 620083, Russian Federationen
local.identifier.pure12459365-
local.identifier.eid2-s2.0-85090541548-
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