TY - JOUR

T1 - Exponential Consensus of Multiple Agents Over Dynamic Network Topology

T2 - Controllability, Connectivity, and Compactness

AU - Ma, Qichao

AU - Qin, Jiahu

AU - Anderson, Brian D.O.

AU - Wang, Long

N1 - Publisher Copyright:
© 1963-2012 IEEE.

PY - 2023/12/1

Y1 - 2023/12/1

N2 - This paper investigates the problem of securing exponentially fast consensus (exponential consensus for short) for identical agents with finite dimensional linear system dynamics over dynamic network topology. Our aim is to find the weakest possible conditions that guarantee exponential consensus using a Lyapunov function consisting of a sum of terms of the same functional form. We first investigate necessary conditions, starting by examining the system parameters. It is found that controllability of the linear agents is necessary for achieving consensus. Then, to work out necessary conditions incorporating the network topology, we construct a set of Laplacian matrix-valued functions. The precompactness of this set of functions is shown to be a significant generalization of existing assumptions on network topology. With the aid of such a precompactness assumption and restricting the Lyapunov function to one consisting of a sum of terms of the same functional form, we prove that a joint (δ, T)-connectivity condition on the network topology is necessary for exponential consensus. Finally, we investigate how the above two 'necessities' work together to guarantee exponential consensus. To partially address this problem, we define a synchronization index to characterize the interplay between agent parameters and network topology. Based on this notion, it is shown that by designing a proper feedback matrix and under the precompactness assumption, exponential consensus can be reached globally and uniformly if the joint (δ,T)-connectivity and controllability conditions are satisfied, and the synchronization index is not less than one.

AB - This paper investigates the problem of securing exponentially fast consensus (exponential consensus for short) for identical agents with finite dimensional linear system dynamics over dynamic network topology. Our aim is to find the weakest possible conditions that guarantee exponential consensus using a Lyapunov function consisting of a sum of terms of the same functional form. We first investigate necessary conditions, starting by examining the system parameters. It is found that controllability of the linear agents is necessary for achieving consensus. Then, to work out necessary conditions incorporating the network topology, we construct a set of Laplacian matrix-valued functions. The precompactness of this set of functions is shown to be a significant generalization of existing assumptions on network topology. With the aid of such a precompactness assumption and restricting the Lyapunov function to one consisting of a sum of terms of the same functional form, we prove that a joint (δ, T)-connectivity condition on the network topology is necessary for exponential consensus. Finally, we investigate how the above two 'necessities' work together to guarantee exponential consensus. To partially address this problem, we define a synchronization index to characterize the interplay between agent parameters and network topology. Based on this notion, it is shown that by designing a proper feedback matrix and under the precompactness assumption, exponential consensus can be reached globally and uniformly if the joint (δ,T)-connectivity and controllability conditions are satisfied, and the synchronization index is not less than one.

KW - Controllable linear systems

KW - dynamic network topology

KW - exponential consensus

KW - necessary and sufficient condition

KW - precompactness

UR - http://www.scopus.com/inward/record.url?scp=85149360788&partnerID=8YFLogxK

U2 - 10.1109/TAC.2023.3245021

DO - 10.1109/TAC.2023.3245021

M3 - Article

SN - 0018-9286

VL - 68

SP - 7104

EP - 7119

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 12

ER -