Based on the sliding-mode and adaptive control theories, the distributed consensus tracking problem under directed topology is investigated for multiple mechanical systems in the presence of general disturbances. We consider that only a subset of the follower mechanical systems can get the information from the dynamic leader mechanical system. First, with the upper bounds of the general disturbances and the leader’s acceleration, a distributed sliding-mode tracking scheme is proposed. Then, when considering the high conservation of sliding-mode control, an improved algorithm with adaptation laws for the upper bounds is developed. Both the proposed algorithms can make tracking errors for each follower mechanical system asymptotically stable. Numerical examples and comparisons are provided to show the effectiveness and the performance of the proposed control strategies.
FaxJMurrayR. Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control2004; 49: 1465–1476.
2.
ZhuSWangDLowCB. Cooperative control of multiple UAVs for moving source seeking. J Intell Robot Syst2014; 74: 333–346.
3.
ShiLCapponiAJohanssonKet al.Resource optimization in a wireless sensor network with guaranteed estimator performance. IET Contr Theory Appl2010; 4: 710–723.
4.
HouZGChengLTanM. Decentralized robust adaptive control for the multiagent system consensus problem using neural networks. IEEE Trans Syst Man Cybern Part B-Cybern2009; 39: 636–647.
5.
BianWFrenchMPruegel-BennettA. Stability for network flow control against disturbances and time delays. SIAM J Control Optim2013; 51: 1063–1098.
6.
ZhaiGHuangC. A note on basic consensus problems in multi-agent systems with switching interconnecting graphs. Int J Control2015; 88: 631–639.
7.
MinHSunFWangS. Distributed adaptive consensus algorithm for networked Euler-Lagrange systems. IET Control Theory Appl2010; 5: 145–154.
8.
ChengLHouZGTanMet al.Neural-network-based adaptive leader-following control for multi-agent systems with uncertainties. IEEE Trans Neural Netw2010; 21: 1351–1358.
9.
Sira-RamirezHCastro-LinaresRPuriel-GilG. An active disturbance rejection approach to leader-follower controlled formation. Asian J Control2014; 16: 382–395.
10.
HongYGHuJPGaoLX. Tracking control for multi-agent consensus with an active leader and variable topology. Automatica2006; 42: 1177–1182.
11.
CaoYCRenWEgerstedtM. Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks. Automatica2012; 48: 1586–1597.
12.
CaoYCRenW. Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Trans Autom Control2012; 57: 33–48.
13.
HongYChenGRBushnellL. Distributed observers design for leader following control of multi-agent. Automatica2008; 44: 846–850.
14.
ChengYLXieDM. Distributed observer design for bounded tracking control of leader-follower multi-agent systems in a sampled-data setting. Int J Control2014; 87: 41–51.
15.
ChenYYTianYP. Directed coordinated control for multi-agent formation motion on a set of given curves. Acta Autom Sin2009; 35: 1541–1549.
16.
Tan FX, Liu DR and Guan XP. Consensus value of multi-agent networked systems with time-delay. In: IEEE/INFORMS International conference on service operations, logistics and informatics, Qinhuangdao, China, 2009.
17.
MunzUPapachristodoulouAAllgowerF. Consensus in multi-agent systems with coupling delays and switching topology. IEEE Trans Autom Control2011; 56: 2976–2982.
18.
ZhaoLJiaYM. Neural network-based adaptive consensus tracking control for multi-agent systems under actuators faults. Int J Syst Sci2016; 47: 1931–1942.
19.
KovacicIMickensRE. Design of nonlinear isochronous oscillators. Nonlinear Dyn2015; 81: 53–61.
20.
TuttyOBlackwellMRogersEet al.Iterative learning control for improved aerodynamic load performance of wind turbines with smart rotors. IEEE Trans. Control Syst Technol2014; 22: 967–979.
21.
GalambosPBaranyiPArzG. Tensor product model transformation based control design for force reflecting tele-grasping under time delay. Proc IMechE, Part C: J Mechanical Engineering Science2014; 228: 756–777.
22.
ChungSJSlotineJE. Cooperative robot control and concurrent synchronization of Lagrangian systems. IEEE Trans Robot2009; 25: 686–700.
23.
HouZGChengLTanMDistributed adaptive coordinated control of multi-manipulator systems using neural networks. In: LiuHet al. (eds). Robot intelligence, London: Springer, 2010, pp. 49–69.
24.
XuWZhouZPhamDT. Hybrid congestion control for high-speed networks. J Netw Comput Appl2011; 34: 1416–1428.
25.
DongWJ. On consensus algorithms of multiple uncertain mechanical systems with a reference trajectory. Automatica2011; 47: 2023–2038.
26.
Feng Z and Hu GQ. Distributed coordinated tracking control for multiple unknown nonlinear Euler-Lagrange systems. In: IEEE international conference on control and automation, Hangzhou, China, 2013.
27.
RenW. Distributed leaderless consensus algorithms for networked Euler-Lagrange systems. Int J Control2009; 82: 2137–2149.
28.
LiuYMinHBWangSC. Distributed consensus of a class of networked heterogeneous multi-agent systems. J Frankl Inst-Eng Appl Math2014; 351: 1700–1716.
29.
WangHLXieYC. Flocking of networked mechanical systems on directed topologies: A new perspective. Int J Control2015; 88: 872–884.
30.
CaiHHuangJ. Leader-following consensus of multiple uncertain Euler–Lagrange systems under switching network topology. Int J Gen Syst2014; 43: 294–304.
31.
MinHBLiuZGLiuY. Coordination control of networked Euler-Lagrange systems with possible switching topology. Acta Autom Sin2013; 39: 1003–1010.
32.
MengZYLinZLRenW. Leader-follower swarm tracking for networked Lagrange systems. Syst Control Lett2012; 61: 117–126.
33.
Cheng L, Hou ZG and Tan M. Decentralized adaptive leader-follower control of multi-manipulator system with uncertain dynamics. In: Proceedings of the 34th annual conference of the IEEE industrial electronics society, Orlando, USA, 2008.
34.
Cheng L, Hou ZG and Tan M. Decentralized adaptive consensus control for multi-manipulator system with uncertain dynamics. In: Proceedings of IEEE international conference on systems, man, and cybernetics, Singapore, 2008.
35.
MeiJZhangHBMaGF. Adaptive coordinated tracking for networked Euler-Lagrange systems under a directed graph. Acta Autom Sin2011; 37: 596–603.
36.
HomRAJohnsonCR. Matrix analysis, Cambridge: Cambridge University Press, 2012, pp. 294–300.
37.
KhooSXieLH. Robust finite-time consensus tracking algorithm for multirobot systems. IEEE-ASME Trans Mechatron2009; 14: 219–228.
38.
LiHLiaoXChenG. Leader-following finite-time consensus in second-order multi-agent networks with nonlinear dynamics. Int J Control Autom Syst2013; 11: 422–426.
