TY - JOUR
T1 - Consensus of discrete-time linear multi-agent systems with observer-type protocols
AU - Li, Zhongkui
AU - Duan, Zhisheng
AU - Chen, Guanrong
PY - 2011/9
Y1 - 2011/9
N2 - This paper concerns the consensus of discrete-time multi-agent systems with linear or linearized dynamics. An observer-type protocol based on the relative outputs of neighboring agents is proposed. The consensus of such a multi-agent system with a directed communication topology can be cast into the stability of a set of matrices with the same low dimension as that of a single agent. The notion of discrete-time consensus region is then introduced and analyzed. For neurally stable agents, it is shown that there exists an observer-type protocol having a bounded consensus region in the form of an open unit disk, provided that each agent is stabilizable and detectable. An algorithm is further presented to construct a protocol to achieve consensus with respect to all the communication topologies containing a spanning tree. Moreover, for the case where the agents have no poles outside the unit circle, an algorithm is proposed to construct a protocol having an origin-centered disk of radius δ (0 > δ <1) as its consensus region. Finally, the consensus algorithms are applied to solve formation control problems of multi-agent systems.
AB - This paper concerns the consensus of discrete-time multi-agent systems with linear or linearized dynamics. An observer-type protocol based on the relative outputs of neighboring agents is proposed. The consensus of such a multi-agent system with a directed communication topology can be cast into the stability of a set of matrices with the same low dimension as that of a single agent. The notion of discrete-time consensus region is then introduced and analyzed. For neurally stable agents, it is shown that there exists an observer-type protocol having a bounded consensus region in the form of an open unit disk, provided that each agent is stabilizable and detectable. An algorithm is further presented to construct a protocol to achieve consensus with respect to all the communication topologies containing a spanning tree. Moreover, for the case where the agents have no poles outside the unit circle, an algorithm is proposed to construct a protocol having an origin-centered disk of radius δ (0 > δ <1) as its consensus region. Finally, the consensus algorithms are applied to solve formation control problems of multi-agent systems.
KW - Consensus
KW - Consensus region
KW - Discrete-time linear system
KW - Formation control
KW - Multi-agent system
KW - Observer- type protocol
UR - http://www.scopus.com/inward/record.url?scp=79960353835&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-79960353835&origin=recordpage
U2 - 10.3934/dcdsb.2011.16.489
DO - 10.3934/dcdsb.2011.16.489
M3 - 21_Publication in refereed journal
VL - 16
SP - 489
EP - 505
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 2
ER -