Strong consensus of convex second‐order multi‐agent systems with time‐varying topologies

Abstract

SummaryThis paper addresses the strong consensus problem of convex second‐order discrete‐time multi‐agent systems (MASs) with time‐varying topologies. The convex second‐order discrete‐time MAS model is derived from the Langevin equation and therefore has a certain physical significance. The strong consensus here means that all the first‐ and second‐order states converge to an identical value. Some fully distributed control protocols are designed with time‐varying weights randomly chosen from an arbitrary finite set. These protocols are applicable to several cases where changing topologies may be directed or undirected, and connected or disconnected. As a special case, the condition for convex second‐order MASs with fixed topologies to achieve the strong consensus is presented. Finally, two simulation examples illustrate the proposed results.