In this paper, group multiple lags consensus of fractional-order leader-following multi-agent systems with nonlinear dynamics are investigated, in which two kinds of lag consensus are considered. One is said to be outergroup lag consensus, which means that different group leaders reach lag consensus. The other one is called innergroup lag consensus, that is to say, the followers will reach lag consensus with their own group leader. Based on Mittag–Leffler stability for fractional-order systems, algebraic graph theory, a class of novel control protocols is designed and the corresponding sufficient conditions are derived to guarantee the achievement of group multiple lags consensus. Furthermore, considering parametric uncertainties, an adaptive control technology is employed to solve the group multiple lags consensus for fractional order multi-agent systems, and the corresponding adaptive control protocols and sufficient conditions are proposed. Finally, numerical simulations are given to demonstrate the effectiveness of the obtained results.
BaiJWenGRahmaniAet al. (2017) Distributed consensus tracking for the fractional-order multi-agent systems based on the sliding mode control method. Neurocomputing235: 210–216.
2.
ChengLWangYRenWet al. (2016a) Containment control of multiagent systems with dynamic leaders based on a pin-type approach. IEEE Transactions on Cybernetics46(12): 3004–3017.
3.
ChengLWangYRenWet al. (2016b) On convergence rate of leader-following consensus of linear multi-agent systems with communication noises. IEEE Transactions on Automatic Control61(11): 3586–3592.
4.
ChuXPengZWenGet al. (2017) Distributed formation tracking of multi-robot systems with nonholonomic constraint via event-triggered approach. Neurocomputing275: 121–131.
5.
CohenIGoldingIRonIGet al. (2001) Biofluiddynamics of lubricating bacteria. Mathematical Methods in the Applied Sciences24(17–18): 1429–1468.
6.
ConsoliniLMorbidiFPrattichizzoDet al. (2008) Leader-follower formation control of nonholonomic mobile robots with input constraints. Automatica44(5): 1343–1349.
7.
DongXHuG (2016) Time-varying formation control for general linear multi-agent systems with switching directed topologies. Automatica73: 47–55.
8.
DongXHuG (2017) Time-varying formation tracking for linear multiagent systems with multiple leaders. IEEE Transactions on Automatic Control62(7): 3658–3664.
9.
Duarte–MermoudMAAguila–CamachoNGallegosJAet al. (2015) Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Communications in Nonlinear Science and Numerical Simulation22(1–3): 650–659.
10.
FaxJAMurrayRM (2004) Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control49(9): 1465–1476.
11.
GabanoJDPoinotT (2011) Fractional modelling and identification of thermal systems. Signal Processing91(3): 531–541.
12.
GaoYYuJYuMet al. (2017) Couple-group consensus for second-order multi-agent systems with the effect of second-order neighbours information. Transactions of the Institute of Measurement and Control40: 1726–1737.
13.
HuQJiangBZhangY (2017) Observer-based output feedback attitude stabilization for spacecraft with finite-time convergence. IEEE Transactions on Control Systems Technology (99): 1–9.
14.
HuQShaoXChenWH (2018a) Robust fault-tolerant tracking control for spacecraft proximity operations using time-varying sliding mode. IEEE Transactions on Aerospace and Electronic Systems54(1): 2–17.
15.
HuQShaoXGuoL (2018b) Adaptive fault-tolerant attitude tracking control of spacecraft with prescribed performance. IEEE/ASME Transactions on Mechatronics23(1): 331–341.
16.
KozlovskyYCohenIGoldingIet al. (1999) Lubricating bacteria model for branching growth of bacterial colonies. Physical Review E: Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics59(6): 703–705.
17.
LiYChenYPodlubnyI (2009) Mittagcleffler stability of fractional order nonlinear dynamic systems. Automatica45(8): 1965–1969.
18.
LiuCLLiuF (2015) Adaptive consensus algorithms for heterogeneous first-order multi-agent systems with diverse nominal velocities. Transactions of the Institute of Measurement and Control38(11): 125–134.
19.
LiuZGuanZShenXet al. (2012) Consensus of multi-agent networks with aperiodic sampled communication via impulsive algorithms using position-only measurements. IEEE Transactions on Automatic Control57(10): 2639–2643.
20.
LiuZYuXGuanZet al. (2017) Pulse-modulated intermittent control in consensus of multiagent systems. IEEE Transactions on Systems Man and Cybernetics Systems47(5): 783–793.
21.
MaZWangYLiX (2015) Cluster-delay consensus in first-order multi-agent systems with nonlinear dynamics. Nonlinear Dynamics83(3): 1303–1310.
22.
MeiJRenWMaG (2013) Distributed coordination for second-order multi-agent systems with nonlinear dynamics using only relative position measurements. Automatica49(5): 1419–1427.
23.
MiaoGMaQ (2015) Group consensus of the first-order multi-agent systems with nonlinear input constraints. Neurocomputing161: 113–119.
24.
Olfati–SaberR (2006) Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Transactions on Automatic Control51(3): 401–420.
25.
Olfati–SaberRMurrayRM (2002) Distributed cooperative control of multiple vehicle formations using structural potential functions. In: IFAC world congress, volume 15, Barcelona, Spain, 21–26 July 2002, pp. 242–248. Laxenburg, Austria: Citeseer.
26.
Olfati–SaberRMurrayRM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control49(9): 1520–1533.
27.
PengZWenGRahmaniAet al. (2013) Leader-follower formation control of nonholonomic mobile robots based on a bioinspired neurodynamic based approach. Robotics and Autonomous Systems61(9): 988–996.
28.
PengZYangSWenGet al. (2016) Adaptive distributed formation control for multiple nonholonomic wheeled mobile robots. Neurocomputing173: 1485–1494.
29.
PorfiriMRobersonDGStilwellDJ (2007) Tracking and formation control of multiple autonomous agents: A two-level consensus approach. Automatica43(8): 1318–1328.
30.
RenWAtkinsE (2007) Distributed multi-vehicle coordinated control via local information exchange. International Journal of Robust and Nonlinear Control17(10–11): 1002–1033.
31.
RenWBeardRW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control50(5): 655–661.
32.
ReynoldsCW (1987) Flocks, herds and schools: A distributed behavioral model. ACM Siggraph Computer Graphics21(4): 25–34.
33.
SongQLiuFWenGet al. (2017) Distributed position-based consensus of second-order multiagent systems with continuous/intermittent communication. IEEE Transactions on Cybernetics47(8): 1860–1871.
34.
SuHWangXLinZ (2009) Flocking of multi-agents with a virtual leader. IEEE Transactions on Automatic Control54(2): 293–307.
35.
WangBJianJShenY (2014) Consensus of fractional-order multi-agent systems with input delays and compounded orders. In: Chinese control conference, Nanjing, China, 28–30 July 2014, pp. 1110–1114. Beijing, China.
36.
WenGHuangJPengZet al. (2016a) On pinning group consensus for heterogeneous multi-agent system with input saturation. Neurocomputing207: 623–629.
37.
WenGYuYPengZet al. (2016b) Consensus tracking for second-order nonlinear multi-agent systems with switching topologies and a time-varying reference state. International Journal of Control89(10): 2096–2106.
38.
WenGYuYPengZet al. (2016c) Dynamical group consensus of heterogenous multi-agent systems with input time delays. Neurocomputing175: 278–286.
39.
WenGYuWLiZet al. (2017a) Neuro-adaptive consensus tracking of multiagent systems with a high-dimensional leader. IEEE Transactions on Cybernetics47(7): 1730–1742.
40.
WenGYuWXiaYet al. (2017b) Distributed tracking of nonlinear multiagent systems under directed switching topology: An observer-based protocol. IEEE Transactions on Systems, Man, and Cybernetics: Systems47(5): 869–881.
41.
XiaHHuangTShaoJet al. (2016) Group consensus of multi-agent systems with communication delays. Neurocomputing171: 1666–1673.
42.
XieGWangL (2007) Consensus control for a class of networks of dynamic agents. International Journal of Robust and Nonlinear Control17(10–11): 941–959.
43.
XingMDengF (2017) Scaled consensus for multi-agent systems with communication time delays. Transactions of the Institute of Measurement and Control40(8): 2651–2659.
44.
XuCZhengYSuHet al. (2014) Necessary and sufficient conditions for distributed containment control of multi-agent systems without velocity measurement. IET Control Theory and Applications8(16): 1752–1759.
45.
YuWRenWZhengGet al. (2013) Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics. Automatica49(7): 2107–2115.
46.
YuWWangHChengFet al. (2017) Second-order consensus in multiagent systems via distributed sliding mode control. IEEE Transactions on Cybernetics47(8): 1872–1881.
47.
YuZJiangHHuC (2015) Leader-following consensus of fractional-order multi-agent systems under fixed topology. Neurocomputing149: 613–620.
