Sign‐consensus over cooperative‐antagonistic networks with switching topologies

Abstract

Summary This paper studies sign consensus, a collective behavior of multiagent systems, when both cooperative and antagonistic interactions coexist among agents. By sign consensus, it means that the states of all agents will eventually achieve the same sign but may with different magnitudes. Compared with some recent works on sign‐consensus problems, where only fixed graphs are considered and the graph adjacency matrix needs to be eventually positive, this paper allows the graph to be switching over time. Control laws are proposed and analyzed with respect to three classes of switching graphs. Examples illustrate the efficacy of the control algorithms.

Output sign‐consensus of heterogeneous multiagent systems over fixed and switching signed graphs

“…This phenomena for general linear multiagent systems is called sign‐consensus in Reference , where the signed graph is fixed and eventually positive. Very recently, sign‐consensus problem of homogeneous multiagent systems is investigated over switching signed graphs …”

“…Very recently, sign-consensus problem of homogeneous multiagent systems is investigated over switching signed graphs. 23,24 Although homogeneity of system dynamics may ease the theoretical analysis, in practice, all multiagent systems are inherently heterogenous, that is, all agents may have different dynamics. For example, two robots are hardly identical in every aspect.…”

Sign‐Consensus of Linear Multiagent Systems under a State Observer Protocol

“…In fact, studies on structurally unbalanced signed digraph have already been reported in [14,15,[19][20][21][22][23][24], etc. In [14,15], agents converge to zero in mean square under arbitrary initial conditions.…”

“…In the pioneering work [23], it is shown that, for the linear timeinvariant (LTI) MASs, if the graph adjacency matrix is eventually positive, sign-consensus is achieved under a state feedback sign-consensus protocol and a fully distributed sign-consensus protocol, respectively. e xed signed digraph in [23] is extended in [24] to being switched over time. Sign-consensus protocols are proposed for three types of time-varying graphs, respectively.…”

“…It is shown that signconsensus can be reached if the graph adjacency matrix is frequently eventually positive. We notice that both works [23,24] propose state feedback-type sign-consensus protocols. However, in reality, due to constraints on measurement, it is usually hard to directly measure agents' states, but only the state estimates are available.…”