×

zbMATH — the first resource for mathematics

Distributed formation control of networked Euler-Lagrange systems with fault diagnosis. (English) Zbl 1307.93032
Summary: A distributed leader-follower formation tracking controller is presented in this paper. The dynamics of each agent is modeled by Euler-Lagrange equations, and all agents are guaranteed to track a desired time-varying trajectory in the workspace. The system uncertainties and external disturbances, which are equivalently described by a bounded additive noise, are considered in the controller design, and the proposed controller is robust to noise. Fault diagnosis of the nonlinear multi-agent system is also discussed with the help of differential geometry tools and an active fault recovery strategy is incorporated into the proposed control scheme. The effectiveness of the proposed controller is verified through simulations.

MSC:
93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93C41 Control/observation systems with incomplete information
93C73 Perturbations in control/observation systems
Software:
Boids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] C.W. Reynolds, Flocks, herds and schools: a distributed behavioral model, in: Proceedings of ACM SIGGRAPH Conference, Anaheim, CA, USA, July 27-31, 1987, pp. 25-34.
[2] Olfati-Saber, R., Flocking for multi-agent dynamic systemsalgorithms and theory, IEEE Trans. Autom. Control, 51, 3, 401-420, (2006) · Zbl 1366.93391
[3] Lynch, N. A., Distributed algorithms, (1996), Morgan Kaufmann San Francisco, CA · Zbl 0877.68061
[4] DeGroot, M. H., Reaching a consensus, J. Am. Stat. Assoc., 69, 345, 118-121, (1974) · Zbl 0282.92011
[5] Witten, T. A.; Sander, L. M., Diffusion-limited aggregation, a kinetic critical phenomenon, Phys. Rev. Lett., 47, 19, 1400-1403, (1981)
[6] Sun, D.; Shao, X.; Feng, G., Position synchronization of multiple motion axes with adaptive coupling control, Automatica, 39, 6, 997-1005, (2003) · Zbl 1137.93366
[7] Sun, D.; Shao, X.; Feng, G., A model-free cross-coupled control for position synchronization of multi-axis motionstheory and experiments, IEEE Trans. Control Syst. Technol., 15, 2, 306-314, (2007)
[8] Shan, J.; Liu, H.; Nowotny, S., Synchronised trajectory-tracking control of multiple 3-dof experimental helicopters, IEE Proc. Control Theory Appl., 152, 6, 683-692, (2005)
[9] L. Ma, H. Min, S. Wang, Y. Liu, Consensus of nonlinear multi-agent systems with self and communication time delays: a unified framework, J. Frankl. Inst., in press, 10.1016/j.jfranklin.2014.05.010. · Zbl 1307.93033
[10] Peng, J.; Ye, X., Distributed adaptive controller for the output-synchronization of networked systems in semi-strict feedback form, J. Frankl. Inst., 351, 1, 412-428, (2014) · Zbl 1293.93054
[11] Li, Z.; Ren, W.; Liu, X.; Fu, M., Consensus of multi-agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols, IEEE Trans. Autom. Control, 58, 7, 1786-1791, (2013) · Zbl 1369.93032
[12] Mu, X.; Xiao, X.; Liu, K.; Zhang, J., Leader-following consensus of multi-agent systems with jointly connected topology using distributed adaptive protocols, J. Frankl. Inst., 351, 12, 5399-5410, (2014) · Zbl 1393.93011
[13] Atrianfar, H.; Haeri, M., Adaptive flocking control of nonlinear multi-agent systems with directed switching topologies and saturation constraints, J. Frankl. Inst., 350, 6, 1545-1561, (2013) · Zbl 1293.93041
[14] Ma, Q.; Wang, Z.; Miao, G., Second-order group consensus for multi-agent systems via pinning leader-following approach, J. Frankl. Inst., 351, 3, 1288-1300, (2014) · Zbl 1395.93020
[15] Wan, X.; Xu, L.; Fang, H.; Yang, F.; Li, X., Exponential synchronization of switched genetic oscillators with time-varying delays, J. Frankl. Inst., 351, 8, 4395-4414, (2014) · Zbl 1294.93009
[16] Li, H.; Ming, C.; Shen, S.; Wong, W., Event-triggered control for multi-agent systems with randomly occurring nonlinear dynamics and time-varying delay, J. Frankl. Inst., 351, 5, 2582-2599, (2014) · Zbl 1372.93020
[17] Liu, Y.; Min, H.; Wang, S.; Ma, L.; Liu, Z., Consensus for multiple heterogeneous Euler-Lagrange systems with time-delay and jointly connected topologies, J. Frankl. Inst., 351, 6, 3351-3363, (2014) · Zbl 1290.93007
[18] Liu, Y.; Min, H.; Wang, S.; Liu, Z.; Liao, S., Distributed consensus of a class of networked heterogeneous multi-agent systems, J. Frankl. Inst., 351, 3, 1700-1716, (2014) · Zbl 1395.93059
[19] Sundaram, S.; Hadjicostis, C. N., Distributed function calculation via linear iterative strategies in the presence of malicious agents, IEEE Trans. Autom. Control, 56, 7, 1495-1508, (2011) · Zbl 1368.93140
[20] M. Franceschelli, M. Egerstedt, A. Giua, Motion probes for fault detection and recovery in networked control systems, in: Proceedings of the 2008 American Control Conference, Seattle, WA, USA, June 11-13, 2008, pp. 4358-4363.
[21] M. Franceschelli, A. Giua, C. Seatzu, Decentralized fault diagnosis for sensor networks, in: Proceedings of the 2009 IEEE International Conference on Automation Science and Engineering, Bangalore, India, August 22-25, 2009, pp. 334-339.
[22] Ren, W., Distributed leaderless consensus algorithms for networked Euler-Lagrange systems, Int. J. Control, 82, 11, 2137-2149, (2009) · Zbl 1175.93074
[23] J. Mei, W. Ren, G. Ma, Containment control for multiple Euler-Lagrange systems with parametric uncertainties in directed networks, in: Proceedings of 2011 American Control Conference, San Francisco, CA, USA, June 29-July 1, 2011, pp. 2186-2191.
[24] Cortes, J.; Martinez, S.; Bullo, F., Spatially-distributed coverage optimization and control with limited-range interactions, ESAIM: Control Optim. Calc. Var., 11, 691-719, (2005) · Zbl 1080.90070
[25] Cortes, J., Discontinuous dynamical systems - a tutorial on solutions, nonsmooth analysis, and stability, IEEE Control Syst. Mag., 28, 3, 36-73, (2008) · Zbl 1395.34023
[26] Filippov, A. F.; Arscott, F. M., Differential equations with discontinuous righthand sides, (1988), Kluwer Academic Dordrecht, The Netherlands
[27] Dieci, L.; Lopez, L., Sliding motion in Filippov differential systemstheoretical results and a computational approach, SIAM J. Numer. Anal., 47, 3, 2023-2051, (2009) · Zbl 1197.34009
[28] Ren, W.; Beard, R., Distributed consensus in multi-vehicle cooperative control, (2008), Springer-Verlag London · Zbl 1144.93002
[29] Shevitz, D.; Paden, B., Lyapunov stability theory of nonsmooth systems, IEEE Trans. Autom. Control, 39, 9, 1910-1914, (1994) · Zbl 0814.93049
[30] Paden, B.; Sastry, S., A calculus for computing filippov◊≥s differential inclusion with application to the variable structure control of robot manipulators, IEEE Trans. Circuits Syst., 34, 1, 73-82, (1987) · Zbl 0632.34005
[31] Loria, A.; Panteley, E.; Nijmeijer, H., A remark on passivity-based and discontinuous control of uncertain nonlinear systems, Automatica, 37, 9, 1481-1487, (2001) · Zbl 0980.93503
[32] Chen, J.; Patton, R. J., Robust model-based fault diagnosis for dynamic systems, (1999), Kluwer Academic Publishers Boston · Zbl 0920.93001
[33] Ding, S. X., Model-based fault diagnosis techniques, (2008), Springer Berlin Heidelberg
[34] Floquet, T.; Barbot, J. P., Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs, Int. J. Syst. Sci., 38, 10, 803-815, (2007) · Zbl 1128.93311
[35] J.A. Moreno, M. Osorio, A Lyapunov approach to second-order sliding mode controllers and observers, in: Proceedings of the 2008 IEEE International Conference on Decision and Control, Cancun, Mexico, December 9-11, 2008, pp. 2856-2861.
[36] Moreno, J. A.; Osorio, M., Strict Lyapunov functions for the super-twisting algorithm, IEEE Trans. Autom. Control, 57, 4, 1035-1040, (2012) · Zbl 1369.93568
[37] Davila, J.; Fridman, L.; Levant, A., Second-order sliding-mode observer for mechanical systems, IEEE Trans. Autom. Control, 50, 11, 1785-1789, (2005) · Zbl 1365.93071
[38] Massoumnia, M.-A., A geometric approach to the synthesis of failure detection filters, IEEE Trans. Autom. Control, 31, 9, 839-846, (1986) · Zbl 0599.93017
[39] Massoumnia, M.-A.; Verghese, G. C.; Willsky, A. S., Failure detection and identification, IEEE Trans. Autom. Control, 34, 3, 316-321, (1989) · Zbl 0682.93061
[40] Bokor, J.; Balas, G., Detection filter design for lpv systems - a geometric approach, Automatica, 40, 3, 511-518, (2004) · Zbl 1042.93018
[41] Isidori, A., Nonlinear control system, (1995), Springer Berlin Heidelberg, New York
[42] Khalil, H., Nonlinear systems, (2002), Prentice Hall Upper Saddle River, NJ
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.