A unifying convex analysis and switching system approach to consensus with undirected communication graphs

Switching between finitely many continuous-time autonomous steepest descent dynamics for convex functions is considered. Convergence of complete solutions to common minimizers of the convex functions, if such minimizers exist, is shown. The convex functions need not be smooth and the dynamics may be...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 111; p. 108598
Main Authors Goebel, Rafal, Sanfelice, Ricardo G.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.01.2020
Subjects
Consensus
Convex analysis
Pointwise asymptotic stability
Steepest descent
Switching system
Steepest descent
Pointwise asymptotic stability
Consensus
Convex analysis
Switching system
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Summary:Switching between finitely many continuous-time autonomous steepest descent dynamics for convex functions is considered. Convergence of complete solutions to common minimizers of the convex functions, if such minimizers exist, is shown. The convex functions need not be smooth and the dynamics may be subject to constraints. Since the common minimizers may represent consensus in a multi-agent system modeled by an undirected communication graph, several known results about asymptotic consensus are deduced as special cases. Extension to a time-varying case is included.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2019.108598