The coupling strength versus convergence speed in pinning control

Nonlinear Dynamics(2019)

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Pinning control, which drives a networked system to a coherent state, has attracted much attention in recent years. The controllability of pinning control is usually characterized by the ratio of the largest to the smallest eigenvalues of the Laplacian relevant matrices. In this paper, we demonstrate that the ratio evaluation cannot precisely characterize the pinning controllability, especially the convergence rate (Lyapunov exponent) of a system. Thus, we propose a method to the pinning controllability from two perspectives: the coupling range and convergence speed. The former represents the synchronization range of the coupling strength between agents. Higher coupling range is better. However, the convergence speed characterizes the convergence rate of the pinning synchronization. Moreover, we analytically show that the classical ratio metric, the coupling range and convergence speed cannot arrive at optimums simultaneously. Comparing with the classical ratio metric, the pinning controllability could be better characterized by the coupling range and convergence speed in analytical and practical ways.
Pinning control,Synchronization,Control strength,Convergence speed
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