TY - JOUR
T1 - Analysis of the Heterogeneous Vectorial Network Model of Collective Motion
AU - Hasanyan, Jalil
AU - Zino, Lorenzo
AU - Truszkowska, Agnieszka
AU - Rizzo, Alessandro
AU - Porfiri, Maurizio
N1 - Funding Information:
Manuscript received June 3, 2020; revised July 16, 2020; accepted July 17, 2020. Date of publication July 20, 2020; date of current version August 4, 2020. This work was supported in part by the National Science Foundation under Grant CMMI-1561134; in part by Mitsui-USA Fundation, Compagnia di San Paolo, MAECI (“Mac2Mic”); in part by European Research Council under Grant ERC-CoG-771687; and in part by the Netherlands Organization for Scientific Research under Grant NWO-vidi-14134. Recommended by Senior Editor J.-F. Zhang. (Corresponding authors: Alessandro Rizzo; Maurizio Porfiri.) Jalil Hasanyan and Agnieszka Truszkowska are with the Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Brooklyn, NY 11201 USA.
Publisher Copyright:
© 2017 IEEE.
PY - 2021/7
Y1 - 2021/7
N2 - We analyze the vectorial network model, a stochastic protocol that describes collective motion of groups of agents, randomly mixing in a planar space. Motivated by biological and technical applications, we focus on a heterogeneous form of the model, where agents have different propensity to interact with others. By linearizing the dynamics about a synchronous state and leveraging an eigenvalue perturbation argument, we establish a closed-form expression for the mean-square convergence rate to the synchronous state in the absence of additive noise. These closed-form findings are extended to study the effect of added noise on the agents' coordination, captured by the polarization of the group. Our results reveal that heterogeneity has a detrimental effect on both the convergence rate and the polarization, which is nonlinearly moderated by the average number of connections in the group. Numerical simulations are provided to support our theoretical findings.
AB - We analyze the vectorial network model, a stochastic protocol that describes collective motion of groups of agents, randomly mixing in a planar space. Motivated by biological and technical applications, we focus on a heterogeneous form of the model, where agents have different propensity to interact with others. By linearizing the dynamics about a synchronous state and leveraging an eigenvalue perturbation argument, we establish a closed-form expression for the mean-square convergence rate to the synchronous state in the absence of additive noise. These closed-form findings are extended to study the effect of added noise on the agents' coordination, captured by the polarization of the group. Our results reveal that heterogeneity has a detrimental effect on both the convergence rate and the polarization, which is nonlinearly moderated by the average number of connections in the group. Numerical simulations are provided to support our theoretical findings.
KW - Stochastic systems
KW - stability of linear systems
KW - time-varying systems
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U2 - 10.1109/LCSYS.2020.3010630
DO - 10.1109/LCSYS.2020.3010630
M3 - Article
AN - SCOPUS:85089699692
VL - 5
SP - 1103
EP - 1108
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
SN - 2475-1456
IS - 3
M1 - 9144519
ER -