Optimal switching between two linear consensus protocols

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider a linear consensus problem with time-varying connectivity modeled as a switched system, switching between two linear consensus subsystems. A natural question is which switching law yields the best (or worst) consensus convergence rate? We formalize this question in the framework of optimal control theory. The linear switched system is relaxed to a bilinear control system, with the control replacing the switching law. A control is said to be optimal if it leads to the best convergence to consensus. We derive a necessary condition for optimality, stated in the form of a maximum principle (MP). We give a complete characterization of the optimal control in the two-dimensional case, while in the three-dimensional case we show that there is always an optimal control that belongs to a subset of "nice" controls. Higher-dimensional systems may be addressed using efficient numerical algorithms for solving optimal control problems.

Original languageEnglish
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1372-1377
Number of pages6
ISBN (Print)9781467357173
DOIs
StatePublished - 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: 10 Dec 201313 Dec 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Conference

Conference52nd IEEE Conference on Decision and Control, CDC 2013
Country/TerritoryItaly
CityFlorence
Period10/12/1313/12/13

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