@prefix vivo: . @prefix edm: . @prefix dcterms: . @prefix dc: . @prefix skos: . @prefix ns0: . vivo:departmentOrSchool "Non UBC"@en ; edm:dataProvider "DSpace"@en ; dcterms:creator "Goebel, Rafal"@en ; dcterms:issued "2018-03-27T05:02:06Z"@*, "2017-09-22T09:40"@en ; dcterms:description """The talk presents some concepts and results from systems and control theory, focusing on convergence to and stability of a continuum of equilibria in a dynamical system.
The well-studied and understood asymptotic stability of a compact set requires Lyapunov stability of the set: solutions that start close remain close to the set, and that every solution converge to the set, in terms of distance. Pointwise asymptotic stability of a set of equilibria requires Lyapunov stability of each equilibrium, and that every solution converge to one of the equilibria. This property is present, for example, in continuous-time steepest descent and convergent saddle-point dynamics, in optimization algorithms generating convergent Fejer monotone sequences, etc., and also in many consensus algorithms for multi-agent systems. The talk will present some background on asymptotic stability and then discuss necessary and sufficient conditions for pointwise asymptotic stability in terms of set-valued Lyapunov functions; robustness of this property to perturbations; and how the property can be achieved in a control system by optimal control."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/64943?expand=metadata"@en ; dcterms:extent "39 minutes"@en ; dc:format "video/mp4"@en ; skos:note ""@en, "Author affiliation: Loyola University Chicago"@en ; edm:isShownAt "10.14288/1.0364485"@en ; dcterms:language "eng"@en ; ns0:peerReviewStatus "Unreviewed"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ; dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ; ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ; ns0:scholarLevel "Faculty"@en ; dcterms:isPartOf "BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))"@en ; dcterms:subject "Mathematics"@en, "Operations research, mathematical programming"@en, "Operator theory"@en, "Control/optimization/operation research"@en ; dcterms:title "Pointwise Asymptotic Stability"@en ; dcterms:type "Moving Image"@en ; ns0:identifierURI "http://hdl.handle.net/2429/64943"@en .