The consensus problem for multiple Euler–Lagrange systems has been extensively studied under various assumptions on the connectivity of the communication graph. In practice, it is desirable to enable the control law the capability of maintaining the connectivity of the communication graph, thus achieving consensus without assuming the connectivity of the communication graph. We call such a problem as consensus with connectivity preservation. In this paper, we will study this problem for multiple uncertain Euler–Lagrange systems. By combining the adaptive control technique and potential function technique, we will show that such a problem is solvable under a set of standard assumptions. By employing different potential functions, our approach will also lead to the solution of such problems as rendezvous and flocking.
Issue Section:
Research Papers
References
1.
Cheah
, C. C.
, Hou
, S. P.
, and Slotine
, J. J. E.
, 2009
, “Region-Based Shape Control for a Swarm of Robots
,” Automatica
, 45
(10
), pp. 2406
–2411
.2.
Spong
, M. W.
, and Vidyasagar
, M.
, 1989
, Robot Dynamics and Control
, Wiley
, New York
.3.
Wang
, H.
, 2012
, “Recursive Composite Adaptation for Robot Manipulators
,” ASME J. Dyn. Syst. Meas. Control
, 135
(2
), p. 021010
.4.
Slotine
, J. J.
, and Li
, W.
, 1991
, Applied Nonlinear Control
, Prentice Hall
, Upper Saddle River, NJ
.5.
Liu
, Y.
, and Chopra
, N.
, 2013
, “Synchronization of Networked Mechanical Systems With Communication Delays and Human Input
,” ASME J. Dyn. Syst. Meas. Control
, 135
(4
), p. 041004
.6.
Nuño
, E.
, Ortega
, R.
, Basañez
, L.
, and Hill
, D.
, 2011
, “Synchronization of Networks of Nonidentical Euler-Lagrange Systems With Uncertain Parameters and Communication Delays
,” IEEE Trans. Autom. Control
, 56
(4
), pp. 935
–941
.7.
Ren
, W.
, 2009
, “Distributed Leaderless Consensus Algorithms for Networked Euler-Lagrange Systems
,” Int. J. Control
, 82
(11
), pp. 2137
–2149
.8.
Wang
, L.
, Meng
, B.
, and Wang
, H.
, 2013
, “Adaptive Task-Space Synchronization of Networked Robotic Agents Without Task-Space Velocity Measurements
,” Int. J. Control
, 87
(2
), pp. 384
–392
.9.
Liu
, Y.
, Min
, H.
, Wang
, S.
, Liu
, Z.
, and Liao
, S.
, 2014
, “Distributed Adaptive Consensus for Multiple Mechanical Systems With Switching Topologies and Time-Varying Delay
,” Syst. Control Lett.
, 64
, pp. 119
–126
.10.
Mehrabian
, A. R.
, and Khorasani
, K.
, 2015
, “Cooperative Optimal Synchronization of Networked Uncertain Nonlinear Euler-Lagrange Heterogeneous Multi-Agent Systems With Switching Topologies
,” ASME J. Dyn. Syst. Meas. Control
, 137
(4), p. 041006
.11.
Min
, H.
, Liu
, Z.
, Liu
, Y.
, Wang
, S.
, and Yang
, Y.
, 2013
, “Coordination Control of Networked Euler-Lagrange Systems With Possible Switching Topology
,” Acta Autom. Sin.
, 39
(7
), pp. 1003
–1010
.12.
Min
, H.
, Sun
, F.
, Wang
, S.
, and Li
, H.
, 2011
, “Distributed Adaptive Consensus Algorithm for Networked Euler-Lagrange Systems
,” IET Control Theory Appl.
, 5
(1
), pp. 145
–154
.13.
Dong
, Y.
, and Huang
, J.
, 2014
, “Cooperative Global Robust Output Regulation for Nonlinear Multi-Agent Systems in Output Feedback Form
,” ASME J. Dyn. Syst. Meas. Control
, 136
(3), p. 031001
.14.
Cao
, Y.
, and Ren
, W.
, 2012
, “Distributed Coordinated Tracking With Reduced Interaction Via a Variable Structure Approach
,” IEEE Trans. Autom. Control
, 57
(1
), pp. 33
–48
.15.
Dimarogonas
, D. V.
, and Johansson
, K. H.
, 2010
, “Bounded Control of Network Connectivity in Multi-Agent Systems
,” IET Control Theory Appl.
, 4
(8
), pp. 1330
–1338
.16.
Ji
, M.
, and Egerstedt
, M.
, 2007
, “Distributed Coordination Control of Multiagent Systems While Preserving Connectedness
,” IEEE Trans. Rob.
, 23
(4
), pp. 693
–703
.17.
Dong
, Y.
, and Huang
, J.
, 2013
, “A Leader-Following Rendezvous Problem of Double Integrator Multi-Agent Systems
,” Automatica
, 49
(5
), pp. 1386
–1391
.18.
Dong
, Y.
, and Huang
, J.
, 2014
, “Leader-Following Connectivity Preservation Rendezvous of Multiple Double Integrator Systems Based on Position Measurement Only
,” IEEE Trans. Autom. Control
, 59
(9
), pp. 2598
–2603
.19.
Su
, H.
, Wang
, X.
, and Chen
, G.
, 2010
, “Rendezvous of Multiple Mobile Agents With Preserved Network Connectivity
,” Syst. Control Lett.
, 59
(5
), pp. 313
–322
.20.
Mao
, Y.
, Dou
, L.
, Fang
, H.
, and Chen
, J.
, 2013
, “Distributed Flocking of Lagrangian Systems With Global Connectivity Maintenance
,” IEEE International Conference on Cyber Technology in Automation, Control and Intelligent Systems
(CYBER
), Nanjing, China, May 26–29, pp. 69
–74
.21.
Dong
, Y.
, and Huang
, J.
, 2014
, “Consensus With Connectivity Preservation of Uncertain Euler-Lagrange Multi-Agent Systems
,” 33rd Chinese Control Conference
(CCC
), Nanjing, China, July 28–30, pp. 1063
–1068
.22.
Cai
, H.
, and Huang
, J.
, 2014
, “Leader-Following Consensus of Multiple Uncertain Euler-Lagrange Systems Under Switching Network Topology
,” Int. J. Gen. Syst.
, 43
(3–4
), pp. 294
–304
.23.
Zavlanos
, M. M.
, Jadbabaie
, A.
, and Pappas
, G. J.
, 2007
, “Flocking While Preserving Network Connectivity
,” 46th IEEE Conference on Decision and Control
, New Orleans, LA, Dec. 12–14, pp. 2919
–2924
.24.
Wang
, H.
, 2014
, “Consensus of Networked Mechanical Systems With Communication Delays: A Unified Framework
,” IEEE Trans. Autom. Control
, 59
(6
), pp. 1571
–1576
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