Publication

Persistent Flows in Deterministic Chains

Xia, W., Shi, G., Meng, Z., Cao, M. & Johansson, K., Jul-2019, In : IEEE Transactions on Automatic Control. 64, 7, p. 2766-2781 16 p.

Research output: Contribution to journalArticleAcademicpeer-review

APA

Xia, W., Shi, G., Meng, Z., Cao, M., & Johansson, K. (2019). Persistent Flows in Deterministic Chains. IEEE Transactions on Automatic Control, 64(7), 2766-2781. https://doi.org/10.1109/TAC.2019.2893974

Author

Xia, Weiguo ; Shi, Guodong ; Meng, Ziyang ; Cao, Ming ; Johansson, Karl. / Persistent Flows in Deterministic Chains. In: IEEE Transactions on Automatic Control. 2019 ; Vol. 64, No. 7. pp. 2766-2781.

Harvard

Xia, W, Shi, G, Meng, Z, Cao, M & Johansson, K 2019, 'Persistent Flows in Deterministic Chains', IEEE Transactions on Automatic Control, vol. 64, no. 7, pp. 2766-2781. https://doi.org/10.1109/TAC.2019.2893974

Standard

Persistent Flows in Deterministic Chains. / Xia, Weiguo; Shi, Guodong; Meng, Ziyang; Cao, Ming; Johansson, Karl.

In: IEEE Transactions on Automatic Control, Vol. 64, No. 7, 07.2019, p. 2766-2781.

Research output: Contribution to journalArticleAcademicpeer-review

Vancouver

Xia W, Shi G, Meng Z, Cao M, Johansson K. Persistent Flows in Deterministic Chains. IEEE Transactions on Automatic Control. 2019 Jul;64(7):2766-2781. https://doi.org/10.1109/TAC.2019.2893974


BibTeX

@article{18f862304e9f4c9bbeb6219ce9194e80,
title = "Persistent Flows in Deterministic Chains",
abstract = "This paper studies the role of persistent flows in the convergence of infinite backward products of stochastic matrices of deterministic chains over networks with non-reciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l1 norm; convergence of the infinite backward products to a rank-one matrix of a deterministic chain of stochastic matrices is equivalent to achieving consensus at the node states. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature, respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place. The results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results. Illustrative examples are provided to validate the results and show the critical importance of the nontrivial lower boundedness of the self-confidence of the agents.",
keywords = "CONTINUOUS-TIME CONSENSUS, SEEKING, COORDINATION, CONVERGENCE, ALGORITHMS, AGREEMENT, SYSTEMS",
author = "Weiguo Xia and Guodong Shi and Ziyang Meng and Ming Cao and Karl Johansson",
year = "2019",
month = "7",
doi = "10.1109/TAC.2019.2893974",
language = "English",
volume = "64",
pages = "2766--2781",
journal = "IEEE-Transactions on Automatic Control",
issn = "0018-9286",
publisher = "IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC",
number = "7",

}

RIS

TY - JOUR

T1 - Persistent Flows in Deterministic Chains

AU - Xia, Weiguo

AU - Shi, Guodong

AU - Meng, Ziyang

AU - Cao, Ming

AU - Johansson, Karl

PY - 2019/7

Y1 - 2019/7

N2 - This paper studies the role of persistent flows in the convergence of infinite backward products of stochastic matrices of deterministic chains over networks with non-reciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l1 norm; convergence of the infinite backward products to a rank-one matrix of a deterministic chain of stochastic matrices is equivalent to achieving consensus at the node states. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature, respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place. The results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results. Illustrative examples are provided to validate the results and show the critical importance of the nontrivial lower boundedness of the self-confidence of the agents.

AB - This paper studies the role of persistent flows in the convergence of infinite backward products of stochastic matrices of deterministic chains over networks with non-reciprocal interactions between agents. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite l1 norm; convergence of the infinite backward products to a rank-one matrix of a deterministic chain of stochastic matrices is equivalent to achieving consensus at the node states. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature, respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place. The results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results. Illustrative examples are provided to validate the results and show the critical importance of the nontrivial lower boundedness of the self-confidence of the agents.

KW - CONTINUOUS-TIME CONSENSUS

KW - SEEKING

KW - COORDINATION

KW - CONVERGENCE

KW - ALGORITHMS

KW - AGREEMENT

KW - SYSTEMS

U2 - 10.1109/TAC.2019.2893974

DO - 10.1109/TAC.2019.2893974

M3 - Article

VL - 64

SP - 2766

EP - 2781

JO - IEEE-Transactions on Automatic Control

JF - IEEE-Transactions on Automatic Control

SN - 0018-9286

IS - 7

ER -

ID: 74332683