×

Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control. (English) Zbl 1338.93039

Summary: In this paper, the leader-follower consensus problem of fractional-order multi-agent systems is considered via adaptive pinning control. The dynamics of leader and all followers with linear and nonlinear functions are investigated, respectively. We assume that the node should be pinned if its in-degree is less than its out-degree in the paper. Under this assumption and based on the stability theory of fractional-order differential systems, some leader-follower consensus criteria are derived, which are easily obtained by matrix inequalities. The control of each agent using local information is designed and a detailed analysis of the leader-followier consensus is presented. The design technique is based on algebraic graph theory and the Riccati inequality. Several simulation examples are presented to demonstrate the effectiveness of the proposed method.

MSC:

93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
34A08 Fractional ordinary differential equations
93C40 Adaptive control/observation systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1093/beheco/arg109 · doi:10.1093/beheco/arg109
[2] DOI: 10.1137/1.9781611970777 · Zbl 0816.93004 · doi:10.1137/1.9781611970777
[3] DOI: 10.1016/j.physa.2012.06.050 · doi:10.1016/j.physa.2012.06.050
[4] DOI: 10.1109/TSMCB.2009.2024647 · doi:10.1109/TSMCB.2009.2024647
[5] DOI: 10.1016/j.sysconle.2010.01.008 · Zbl 1222.93006 · doi:10.1016/j.sysconle.2010.01.008
[6] DOI: 10.1016/j.automatica.2008.12.027 · Zbl 1162.93305 · doi:10.1016/j.automatica.2008.12.027
[7] DOI: 10.1002/mma.190 · Zbl 1097.76618 · doi:10.1002/mma.190
[8] DOI: 10.1137/S0363012903428652 · Zbl 1108.37058 · doi:10.1137/S0363012903428652
[9] DOI: 10.1109/TAC.2007.895897 · Zbl 1366.93401 · doi:10.1109/TAC.2007.895897
[10] Hammel D., Israel Journal of Zoology 41 pp 261– (1995)
[11] Horn R., Topics in matrix analysis (1994) · Zbl 0801.15001
[12] DOI: 10.1016/j.laa.2009.09.012 · Zbl 1181.15024 · doi:10.1016/j.laa.2009.09.012
[13] Kilbas A., Theory and appliciations of fractional differential equations (2006)
[14] DOI: 10.1103/PhysRevE.59.7025 · doi:10.1103/PhysRevE.59.7025
[15] DOI: 10.1016/j.ijleo.2012.10.007 · doi:10.1016/j.ijleo.2012.10.007
[16] DOI: 10.1049/iet-cta.2008.0263 · doi:10.1049/iet-cta.2008.0263
[17] DOI: 10.1109/TNNLS.2013.2247059 · doi:10.1109/TNNLS.2013.2247059
[18] DOI: 10.1002/rnc.1531 · Zbl 1204.93043 · doi:10.1002/rnc.1531
[19] DOI: 10.1049/iet-cta.2011.0649 · doi:10.1049/iet-cta.2011.0649
[20] DOI: 10.1016/j.neucom.2012.10.027 · doi:10.1016/j.neucom.2012.10.027
[21] DOI: 10.1002/rnc.1147 · Zbl 1266.93010 · doi:10.1002/rnc.1147
[22] DOI: 10.1002/asjc.492 · Zbl 1303.93017 · doi:10.1002/asjc.492
[23] DOI: 10.1137/S0895479894276370 · Zbl 0853.15013 · doi:10.1137/S0895479894276370
[24] DOI: 10.1109/TSMCB.2012.2227723 · doi:10.1109/TSMCB.2012.2227723
[25] DOI: 10.1002/asjc.390 · Zbl 1263.93013 · doi:10.1002/asjc.390
[26] DOI: 10.1080/00207170902838269 · Zbl 1178.93013 · doi:10.1080/00207170902838269
[27] DOI: 10.1109/TAC.2007.895948 · Zbl 1366.93414 · doi:10.1109/TAC.2007.895948
[28] DOI: 10.1002/rnc.1144 · Zbl 1266.93013 · doi:10.1002/rnc.1144
[29] DOI: 10.1049/iet-cta.2012.0511 · doi:10.1049/iet-cta.2012.0511
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.