TY - JOUR
T1 - Differential inequalities in multi-agent coordination and opinion dynamics modeling
AU - Proskurnikov, Anton V.
AU - Cao, Ming
PY - 2017
Y1 - 2017
N2 - Many distributed algorithms for multi-agent coordination employ the simple averaging dynamics, referred to as the Laplacian flow. Besides the standard consensus protocols, examples include, but are not limited to, algorithms for aggregation and containment control, target surrounding, distributed optimization and models of opinion formation in social groups. In spite of their similarities, each of these algorithms has been studied using separate mathematical techniques. In this paper, we show that stability and convergence of many coordination algorithms involving the Laplacian flow dynamics follow from the general consensus dichotomy property of a special differential inequality. The consensus dichotomy implies that any solution to the differential inequality is either unbounded or converges to a consensus equilibrium. In this paper, we establish the dichotomy criteria for differential inequalities and illustrate their applications to multi-agent coordination and opinion dynamics modeling.
AB - Many distributed algorithms for multi-agent coordination employ the simple averaging dynamics, referred to as the Laplacian flow. Besides the standard consensus protocols, examples include, but are not limited to, algorithms for aggregation and containment control, target surrounding, distributed optimization and models of opinion formation in social groups. In spite of their similarities, each of these algorithms has been studied using separate mathematical techniques. In this paper, we show that stability and convergence of many coordination algorithms involving the Laplacian flow dynamics follow from the general consensus dichotomy property of a special differential inequality. The consensus dichotomy implies that any solution to the differential inequality is either unbounded or converges to a consensus equilibrium. In this paper, we establish the dichotomy criteria for differential inequalities and illustrate their applications to multi-agent coordination and opinion dynamics modeling.
KW - Complex network
KW - Cooperative control
KW - Distributed algorithm
KW - Multi-agent systems
UR - http://www.scopus.com/inward/record.url?scp=85027885986&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2017.07.065
DO - 10.1016/j.automatica.2017.07.065
M3 - Article
AN - SCOPUS:85027885986
SN - 0005-1098
VL - 85
SP - 202
EP - 210
JO - Automatica
JF - Automatica
ER -