TY - GEN

T1 - Optimal switching between two linear consensus protocols

AU - Ron, Orel

AU - Margaliot, Michael

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84902352586&partnerID=8YFLogxK

U2 - 10.1109/CDC.2013.6760074

DO - 10.1109/CDC.2013.6760074

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AN - SCOPUS:84902352586

SN - 9781467357173

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1372

EP - 1377

BT - 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 52nd IEEE Conference on Decision and Control, CDC 2013

Y2 - 10 December 2013 through 13 December 2013

ER -