Control Localization in Dynamical Systems Connected via a Weighted Tree

We consider the problem of localization of control in dynamical systems coupled via a weighted tree, when only a single system receives control. We abstract this problem into a study of eigenvalues of a perturbed Laplacian matrix. We show that this eigenvalue problem has a complete solution for arbitrarily large control by showing that the best and the worst places to apply control must necessarily be a characteristic vertex and a pendant vertex, respectively. Some partial results are proved in the case of finite control. In particular, we show that a local maximum in localizing the best place for control is also a global maximum. We conjecture in the finite control case that the best place to apply control must also necessarily be a characteristic vertex and present evidence from numerical experiments to support this conjecture.

By: Ravindra Bapat, Chai Wah Wu

Published in: RC25466 in 2014


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