Consensus of fractional multi-agent systems using distributed adaptive protocols. (English) Zbl 1386.93017
Summary: This paper is concerned with the adaptive consensus problem of fractional multi-agent systems for both the linear and nonlinear cases. Distributed adaptive protocols are designed, respectively, for linear and nonlinear fractional multi-agent systems, under which consensus is achieved for any undirected connected communication graph without using any global information. Furthermore, the leader-following problem is studied as an extension. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.
MSC:
| 93A14 | Decentralized systems |
| 68T42 | Agent technology and artificial intelligence |
| 93C40 | Adaptive control/observation systems |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
References:
| [1] | Fax, J and R. Murray, “Information flow and cooperative control of vehicle formations,” IEEE Trans. Autom. Control, Vol. 49, No. 9, pp. 1465-1476 (2004). · Zbl 1365.90056 |
| [2] | Xue, D, JYao, GChen, and Y. Yu, “Formation control of networked multi‐agent systems,” IET Contr. Theory Appl., Vol. 4, No. 10, pp. 2168-2176 (2010). |
| [3] | Wen, G, ZDuan, ZLi, and GChen, “Flocking of multi‐agent dynamical systems with intermittent nonlinear velocity measurements,” Int. J. Robust Nonlinear Control, Vol. 22, No. 16, pp. 1790-1805 (2012). · Zbl 1273.93011 |
| [4] | Jadbabaie, A, JLin, and ASMorse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Trans. Autom. Control, Vol. 48, No. 6, pp. 988-1001 (2003). · Zbl 1364.93514 |
| [5] | Tian, Y. and C.Liu, “Consensus of multi‐agent systems with diverse input and communication delays,” IEEE Trans. Autom. Control, Vol. 53, No. 9, pp. 2122-2128 (2008). · Zbl 1367.93411 |
| [6] | Lv, J and GChen, “A time‐varying complex dynamical network model and its controlled synchronization criteria,” IEEE Trans. Autom. Control, Vol. 50, No. 6, pp. 841-846 (2005). · Zbl 1365.93406 |
| [7] | Yu, W, GChen, and MCao, “Some necessary and sufficient conditions for second‐order consensus in multi‐agent dynamical systems,” Automatica, Vol. 46, No. 6, pp. 1089-1095 (2010). · Zbl 1192.93019 |
| [8] | Ren, W and R.Beard, Distributed consensus in multi‐vehicle cooperative control, Springer‐Verlag, London (2008). · Zbl 1144.93002 |
| [9] | Wen, G, ZDuan, GChen, and WYu, “Consensus tracking of multi‐agent systems with Lipschitz‐type node dynamics and switching topologies,” IEEE Trans. Circuits Syst. I: Regul. Pap., Vol. 61, No. 2, pp. 499-511 (2014). · Zbl 1468.93037 |
| [10] | Li, Z, WRen, XLiu, and MFu, “Consensus of multi‐agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols,” IEEE Trans. Autom. Control, Vol. 58, No. 7, pp. 1786-1791 (2013). · Zbl 1369.93032 |
| [11] | Yu, W, GChen, and MCao, “Consensus in directed networks of agents with nonlinear dynamics,” IEEE Trans. Autom. Control, Vol. 56, No. 6, pp. 1436-1441 (2011). · Zbl 1368.93015 |
| [12] | Song, Q, JCao, and WYu, “Second‐order leader‐following consensus of nonlinear multi‐agent systems via pinning control,” Syst. Control Lett., Vol. 59, No. 9, pp. 553-562 (2010). · Zbl 1213.37131 |
| [13] | Podlubny, I, Fractional differential equations, Academic, New York (1999). · Zbl 0924.34008 |
| [14] | Kilbas, A., H.Srivastava, and JJTrujiilo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006). · Zbl 1092.45003 |
| [15] | Hilfer, R, Applications of Fractional Calculus in Physics, World Scientific, River Edge, NJ (2000). · Zbl 0998.26002 |
| [16] | Bagley, R. and P.Torvik, “A theoretical basis for the application of fractional calculus to viscoelasticity,” J. Theol., Vol. 27, No. 3, pp. 201-210 (1983). · Zbl 0515.76012 |
| [17] | Bagley, R. and P.Torvik, “On the fractional calculus model of viscoelastic behavior,” J. Rheol., Vol. 30, No. 1, pp. 133-155 (1986). · Zbl 0613.73034 |
| [18] | Cao, Y, YLi, WRen, and YChen, “Distributed coordination of networked fractional‐order systems,” IEEE Trans. Sys. Man Cybern Part B, Vol. 40, No. 2, pp. 362-370 (2010). |
| [19] | Yang, H, XZhu, and KCao, “Distributed coordination of fractional order multi‐agent systems with communication delays,” Fract. Calc. Appl. Anal., Vol. 17, No. 1, pp. 23-37 (2014). · Zbl 1312.93086 |
| [20] | Song, C, JCao, and YLiu, “Robust consensus of fractional‐order multi‐agent systems with positive real uncertainty via second‐order neighbors information,” Neurocomputing, Vol. 165, pp. 293-299 (2015). |
| [21] | Sastry, S. and MBodson, Adaptive Control: Stability, Convergence and Robustness, Prentice‐Hall, Englewood Cliffs, NJ (1989). · Zbl 0721.93046 |
| [22] | Shen, J and JLam, “Non‐existence of finite‐time stable equilibria in fractional‐order nonlinear systems,” Automatica, Vol. 50, No. 2, pp. 547-551 (2014). · Zbl 1364.93690 |
| [23] | Yu, J, CHu, HJiang, and XFan, “Projective synchronization for fractional neural networks,” Neural Netw., Vol. 49, pp. 87-95 (2014). · Zbl 1296.34133 |
| [24] | Bao, H, JHPark, and JCao, “Adaptive synchronization of fractional‐order memristor‐based neural networks with time delay,” Nonlinear Dyn., Vol. 82, No. 3, pp. 1343-1354 (2015). · Zbl 1348.93159 |
| [25] | Yu, Z, HJiang, CHu, and JYu, “Leader‐following consensus of fractional‐order multi‐agent systems via adaptive pinning control,” Int. J. Control, Vol. 88, No. 9, pp. 1746-1756 (2015). · Zbl 1338.93039 |
| [26] | Godsil, C and GRoyle, Algebraic Graph Theory. Springer‐Verlag, New York (2001). · Zbl 0968.05002 |
| [27] | Ren, W and YCao, Distributed Coordination of Multi‐agent Networks: Emergent Problems, Models, and Issues, Springer‐Verlag: London (2011). · Zbl 1225.93003 |
| [28] | Norelys, A., M.Duarte‐Mermoud, and J.Gallegos, “Lyapunov functions for fractional order systems,” Commun. Nonlinear Sci. Numer. Simul., Vol. 19, No. 9, pp. 2951-2957 (2014). · Zbl 1510.34111 |
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.
