Development of a distributed consensus algorithm for multiple Euler–Lagrange systems
- Author(s): Lei Liu 1 and Jinjun Shan 1
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View affiliations
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Affiliations:
1:
Department of Earth and Space Science and Engineering, York University, 4700 Keele St., Toronto, M3J 1P3, Canada
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Affiliations:
1:
Department of Earth and Space Science and Engineering, York University, 4700 Keele St., Toronto, M3J 1P3, Canada
- Source:
Volume 9, Issue 2,
19 January 2015,
p.
153 – 162
DOI: 10.1049/iet-cta.2014.0309 , Print ISSN 1751-8644, Online ISSN 1751-8652
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© The Institution of Engineering and Technology
Received
29/08/2013,
Accepted
21/08/2014,
Revised
18/07/2014,
Published
24/09/2014
In this study, a consensus algorithm for multiple non-linear Euler–Lagrange systems is presented. This controller guarantees that all agents can reach a common state in the workspace. External disturbances acting on the system are included in the closed-loop stability analysis, and the input-to-state properties of the proposed controller are investigated based on the concept of input-to-state consensus. Moreover, the influence of structural uncertainty is further discussed on the basis of passivity theory. The robustness of the proposed consensus algorithm is then demonstrated in the presence of both external disturbances and structural uncertainty. Experiments are conducted to validate the effectiveness of the proposed consensus algorithm.
Inspec keywords: uncertain systems; closed loop systems; robust control; distributed control; nonlinear control systems
Other keywords: external disturbances; passivity theory; structural uncertainty; multiple nonlinear Euler-Lagrange systems; closed-loop stability analysis; robustness; distributed consensus algorithm; input-to-state consensus properties
Subjects: Nonlinear control systems; Stability in control theory
References
-
-
1)
- W. Ren . Distributed leaderless consensus algorithms for networked Euler–Lagrange systems. Int. J. Control , 11 , 2137 - 2149
-
2)
-
1. Lynch, N.A.: Distributed Algorithms, 1st edn. (Morgan Kaufmann, 1996)..
-
-
3)
-
23. Gahinet, P., Nemirovski, A., Laub, A., Chilali, M.: ‘LMI Control Toolbox User's Guide’ (The MathWorks, Inc, 1995, 1st edn.).
-
-
4)
-
22. Shi, G., Johansson, K.H.: ‘Robust consensus for continuous-time multiagent dynamics’, SIAM J. Control Optimization, 2013, 51, (5), pp. 3673–3691 (doi: 10.1137/110841308).
-
-
5)
-
30. 3-DOF Helicopter Reference Manual (Quanser Inc, 2010, 1st edn.)..
-
-
6)
- L. Moreau . Stability of multi-agent systems with time-dependent communication links. IEEE Trans. Autom. Control , 2 , 169 - 182
-
7)
-
20. Wang, H.: ‘Passivity based synchronization for networked robotic systems with uncertain kinematics and dynamics’, Automatica, 2013, 49, (3), pp. 755–761 (doi: 10.1016/j.automatica.2012.11.003).
-
-
8)
- R. Olfati-Saber , R.M. Murray . Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control , 9 , 1520 - 1533
-
9)
-
26. Kingston, D.B., Ren, W., Beard, R.W.: ‘Consensus algorithms are input-to-state stable’, Proc. of American Control Conf., Portland, OR, USA, 2005, pp. 1686–1690.
-
-
10)
-
21. Wang, H.: ‘Flocking of networked uncertain Euler-Lagrange systems on directed graphs’, Automatica, 2013, 49, (9), pp. 2774–2779 (doi: 10.1016/j.automatica.2013.05.029).
-
-
11)
-
16. Peng, Z., Wang, D., Liu, H.H., Sun, G.: ‘Neural adaptive control for leader-follower flocking of networked nonholonomic agents with unknown nonlinear dynamics’, Int. J. Adaptive Control Signal Process., p. doi: 10.1002/acs.2400, 2013.
-
-
12)
-
28. Mei, J., Ren, W., Ma, F.G.: ‘Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph’, Automatica, 2012, 48, (4), pp. 653–659 (doi: 10.1016/j.automatica.2012.01.020).
-
-
13)
- T. Vicsek , A. Czirok , E. Ben-Jacob , I. Cohen , O. Shochet . Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. , 1226 - 1229
-
14)
- A. Jadbabaie , J. Lin , A.S. Morse . Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control , 6 , 988 - 1001
-
15)
-
25. Zhou, K.: ‘Essentials of Robust Control’ (Prentice-Hall, 1998, 1st edn.).
-
-
16)
-
18. Liu, Y., Min, H., Wang, S., Liu, Z., Liao, S.: ‘Distributed adaptive consensus for multiple mechanical systems with switching topologies and time-varying delay’, Syst. Control Lett., 2014, 64, pp. 119–126 (doi: 10.1016/j.sysconle.2013.09.005).
-
-
17)
-
17. Mei, J., Ren, W., Chen, J., Ma, G.: ‘Distributed adaptive coordination for multiple Lagrangian systems under a directed graph without using neighbors’ velocity information’, Automatica, 2013, 49, (6), pp. 1723–1731 (doi: 10.1016/j.automatica.2013.02.058).
-
-
18)
-
15. Peng, Z., Wang, D., Zhang, H., Sun, G., Wang, H.: ‘Distributed model reference adaptive control for cooperative tracking of uncertain dynamical multi-agent systems’, IET Control Theory Appl., 2013, 7, (8), pp. 1079–1087 (doi: 10.1049/iet-cta.2012.0765).
-
-
19)
- P. Gahinet , P. Apkarian . A linear matrix inequality approach to H∞ control. Int. J. Robust Nonlinear Control , 421 - 448
-
20)
- W. Ren , R.W. Beard . Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control , 5 , 655 - 661
-
21)
- M.H. DeGroot . Reaching a consensus. J. Am. Stat. Assoc. , 345 , 118 - 121
-
22)
- R.S. Smith , F.Y. Hadaegh . Control of deep-space formation-flying spacecraft; relative sensing and switched information. J. Guid. Control Dynam. , 1 , 106 - 114
-
23)
- P. Gahinet . Explicit controller formulas for LMI-based H∞ synthesis. Automatica , 7 , 1007 - 1014
-
24)
-
27. Khalil, H.: ‘Nonlinear Systems’ (Prentice-Hall, 1996, 2002, 3rd edn.).
-
-
25)
-
6. Tsitsiklis, J.N.: ‘Problems in decentralized decision making and computation’, Ph.D. dissertation, Massachusetts Institute of Technology, Massachusetts, MA, USA, 1984.
-
-
26)
-
12. Ren, W., Beard, R.: ‘Distributed Consensus in Multi-vehicle Cooperative Control’ (Springer-Verlag, 2008, 1st edn.).
-
-
27)
-
33. Laub, A.J.: ‘Matrix Analysis for Scientists and Engineers’ (SIAM: Society for Industrial and Applied Mathematics, 2004, 1st edn.).
-
-
28)
- Z.Y. Lin , B. Francis , M. Maggiore . State agreement for continuous-time coupled nonlinear systems. SIAM J. Control Optim. , 1 , 288 - 307
-
29)
-
28. Lin, W., Shen, T.: ‘Robust passivity and feedback design for minimum-phase nonlinear systems with structural uncertainty’, Automatica, 1999, 35, (1), pp. 35–47 (doi: 10.1016/S0005-1098(98)00120-4).
-
-
30)
- T.A. Witten , L.M. Sander . Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. , 1400 - 3
-
31)
- J.A. Fax , R.M. Murray . Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control , 9 , 1465 - 1476
-
32)
-
29. Marquez, H.J.: ‘Nonlinear control systems: analysis and design’ (John Wiley, 2003, 1st edn.).
-
-
33)
- J. Shan , H.-T. Liu , S. Nowotny . Synchronised trajectory-tracking control of multiple 3-DOF experimental helicopters. IEE Proc. Control Theory Appl. , 683 - 692
-
1)
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