This paper studies the higher-order cluster agreement problem for continuous-time networks evolving over any given directed graph. Necessary and sufficient conditions are derived to reach clusters that are not pre-determined as opposed to existing literature. The analysis shows that appropriate stabilizing choices of coupling strengths do not affect the number of clusters and the final values of the clusters. The results are verified by numerical examples.
AbdessameudATayebiA (2018) Distributed consensus algorithms for a class of high-order multi-agent systems on directed graphs. IEEE Transactions on Automatic Control63(10): 3464–3470.
2.
AkarMShortenR (2008) Distributed probabilistic synchronization algorithms for communication networks. IEEE Transactions on Automatic Control53(1): 389–393.
3.
AnBRLiuGPTanC (2018) Group consensus control for networked multi-agent systems with communication delays. ISA Transactions76: 78–87.
4.
BarnettS (1971) A new formulation of the theorems of hurwitz, routh and sturm. IMA Journal of Applied Mathematics8(2): 240–250.
5.
CaoYSunY (2015) Consensus analysis for third-order multiagent systems in directed networks. Mathematical Problems in Engineering.
6.
ChenYLüJHanFYuX (2011) On the cluster consensus of discrete-time multi-agent systems. Systems & Control Letters60(7): 517–523.
7.
DevelerÜAkarM (2018a) Analysis of cluster consensus in continuous-time networks. In: Annual American Control Conference (ACC), Milwaukee, WI, 27–29 June 2018, pp. 448–453. IEEE.
8.
DevelerÜAkarM (2018b) Input delay effect on cluster consensus in continuous-time networks. IFAC-PapersOnLine51(14): 19–24.
9.
DevelerÜAkarM (2019) Cluster consensus in first and second-order continuous-time networks with input and communication delays. International Journal of Control: 1–29.
10.
ErkanÖFCihanOAkarM (2018) Analysis of distributed consensus protocols with multi-equilibria under time-delays. Journal of the Franklin Institute355(1): 332–360.
11.
HanYLuWChenT (2013) Cluster consensus in discrete-time networks of multiagents with inter-cluster nonidentical inputs. IEEE Transactions on Neural Networks and Learning Systems24(4): 566–578.
12.
HouBSunFLiH, et al. (2015) Observer-based cluster consensus control of high-order multi-agent systems. Neurocomputing168: 979–982.
13.
HouBSunFLiH, et al. (2016) Cluster consensus of high-order multi-agent systems with switching topologies. International Journal of Systems Science47(12): 2859–2868.
14.
JadbabaieALinJMorseAS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control48(6): 988–1001.
15.
JiLLiuQLiaoX (2014) On reaching group consensus for linearly coupled multi-agent networks. Information Sciences287: 1–12.
16.
LiJGuanZHChenG (2015) Multi-consensus of nonlinearly networked multi-agent systems. Asian Journal of Control17(1): 157–164.
17.
MaQWangZMiaoG (2014) Second-order group consensus for multi-agent systems via pinning leader-following approach. Journal of the Franklin Institute351(3): 1288–1300.
18.
Olfati-SaberRMurrayRM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control49(9): 1520–1533.
19.
Olfati-SaberRFaxJAMurrayRM (2007) Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE95(1): 215–233.
20.
QinJYuCAndersonBD (2013) On distributed cluster consensus for multiple double-integrator agents. In: European Control Conference (ECC), Zurich, 17-19 July 2013, pp. 1770–1775. IEEE.
21.
RenWBeardRW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control50(5): 655–661.
22.
RenWMooreKLChenY (2007) High-order and model reference consensus algorithms in cooperative control of multivehicle systems. ASME Journal of Dynamic Systems, Measurement and Control, 129(5): 678–688.
23.
SenelKAkarM (2017a) A distributed coverage adjustment algorithm for femtocell networks. IEEE Transactions on Vehicular Technology66(2): 1739–1747.
24.
SenelKAkarM (2017b) A power allocation algorithm for multi-tier cellular networks with heterogeneous QoS and imperfect channel considerations. IEEE Transactions on Wireless Communications16(11): 7184–7194.
25.
XiaHHuangTZShaoJLYuJY (2016) Group consensus of multi-agent systems with communication delays. Neurocomputing171: 1666–1673.
26.
XieDLiangT (2015) Second-order group consensus for multiagent systems with time delays. Neurocomputing153: 133–139.
27.
XieDShiLJiangF (2018) Group tracking control of secondorder multi-agent systems with fixed and markovian switching topologies. Neurocomputing281: 37–46.
28.
YuJShiY (2017) Scaled group consensus in multiagent systems with first/second-order continuous dynamics. IEEE transactions on cybernetics48(8): 2259–2271.
29.
YuJWangL (2012) Group consensus of multi-agent systems with directed information exchange. International Journal of Systems Science43(2): 334–348.
30.
ZhouBLinZ (2014) Consensus of high-order multiagent systems with large input and communication delays. Automatica50(2): 452–464.
