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dc.contributor.authorAubin, Jean-Pierre
dc.date.accessioned2014-10-30T14:00:36Z
dc.date.available2014-10-30T14:00:36Z
dc.date.issued1990
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14103
dc.language.isoenen
dc.subjectviabilityen
dc.subjectinvarianceen
dc.subjectcontrolled invarianceen
dc.subjectset-valued mapsen
dc.subjectregulation mapen
dc.subjectdifferential inclusionen
dc.subjectfuzzy differential inclusionen
dc.subjectLyapunov stabilityen
dc.subjectasymptotic stabilityen
dc.subjecttrackingen
dc.subjectcontingent coneen
dc.subjectcontingent derivative of a set-valued mapen
dc.subjectepicontingent derivative of a functionen
dc.subject.ddc515en
dc.titleA Survey of Viability Theoryen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenSome theorems of viability theory which are relevant to nonlinear control problems with state constraints and state-dependent control constraints are motivated and surveyed. They all deal with viable solutions to nonlinear control problems, i.e., solutions satisfying at each instant given state constraints of a general and diverse nature. Some classical results on controlled invariance of smooth nonlinear systems are adopted to the nonsmooth case, including inequality constraints bearing on the state and state-dependent constraints on the controls. For instance, existence of a viability kernel of a closed set (corresponding to the largest controlled invariant manifold) is provided under general conditions, even when the zero-dynamics algorithm does not converge. The concepts of slow and heavy viable solutions are introduced, providing concrete ways of regulating viable solutions, by closed-loop feedbacks and closed-loop dynamical feedbacks. Viability theorems also allow the extension of Lyapunov’s second method to nonsmooth observation functions and the construction of “best” Lyapunov functions. As an application, “fuzzy differential inclusion” is presented. Proofs and complements can be found in [Viability Theory, to appear, 1991]. They rely on properties of differential inclusion (see [Differential Inclusions, Springer-Verlag, Berlin, New York, 1984]) and set-valued analysis, (see [Set-Valued Analysis, Birkhäuser, Basel, 1990]).en
dc.relation.isversionofjnlnameSIAM Journal on Control and Optimization
dc.relation.isversionofjnlvol28en
dc.relation.isversionofjnlissue4en
dc.relation.isversionofjnldate1990
dc.relation.isversionofjnlpages749-788en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/0328044en
dc.relation.isversionofjnlpublisherSIAMen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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