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An Adaptive Finite-Time Consensus Control for Higher-Order Nonlinear Multi-agent Systems

  • Sanjoy MondalEmail author
  • Jawhar Ghommam
  • Maarouf Saad
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 79)

Abstract

This chapter presents a finite-time consensus problem of higher-order nonlinear multi-agent systems (MAS) in the presence of bounded disturbances. The nominal control is designed by homogeneous finite-time technique to track the desired target trajectories. The chattering is mitigated by designing an integral sliding surface using adaptive super twisting algorithm (STA). The design parameters of super twisting controller are estimated adaptively without knowing the bounds a priori. The finite time convergence of the consensus protocol for the higher-order MAS is presented using Lyapunov analysis. Simulation results shows the effectiveness of the proposed homogeneous adaptive sliding mode control for the MAS.

Keywords

Higher-order sliding mode Multi-gent system Finite-time convergence Reference tracking Matched uncertainty Adaptive super twisting algorithm 

References

  1. Bhat, S. P., & Bernstein, D. S. (2005). Geometric homogeneity with applications to finite-time stability. Mathematics of Control Signals Systems, 17, 101–127.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Canale, E., Dalmao, F., Mordecki, E., & Souza, M. O. (2015). Robustness of cucker-smale flocking model. IET Control Theory and Applications, 9(3), 346–350.MathSciNetCrossRefGoogle Scholar
  3. Cao, Y., Yu, W., Ren, W., & Chen, G. (2013). An overview of recent progress in the study of distributed multi-agent. An Overview of Recent Progress in the Study of Distributed Multi-agent, 9(1), 427–438.Google Scholar
  4. Consolini, L., Morbidi, F., & Tosques, D. P. M. (2008). Leaderfollower formation control of nonholonomic mobile robots with input constraints. Automatica, 44(5), 1343–1349.MathSciNetCrossRefzbMATHGoogle Scholar
  5. Defoort, M., Floquet, T., Kokosy, A., & Perruquetti, W. (2009). A novel higher order sliding mode control scheme. System and Control Letters, 58, 102–108.MathSciNetCrossRefzbMATHGoogle Scholar
  6. Dimarogonas, D. V., Tsiotras, P., & Kyriakopoulos, K. J. (2009). Leader-follower cooperative attitude control of multiple rigid bodies. Systems and Control Letters, 58, 429–435.Google Scholar
  7. Feng, Y., Han, F., & Yu, X. (2014). Chattering free full-order sliding-mode control. Automatica, 50, 1310–1314.MathSciNetCrossRefzbMATHGoogle Scholar
  8. Ghasemi, M., & Nersesov, S. G. (2014). Finite-time coordination in multiagent systems using sliding mode control approach. Automatica, 50, 1209–1216.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Ghasemi, M., Nersesov, S. G., Clayton, G., & Ashrafiuon, H. (2014a). Sliding mode coordination control for multiagent systems with underactuated agent dynamics. International Journal of Control, 87(12), 2612–2633.MathSciNetCrossRefzbMATHGoogle Scholar
  10. Ghasemi, M., Nersesovn, S. G., & Clayton, G. (2014b). Finite-time tracking using sliding mode control. Journal of the Franklin Institute, 351(5), 2966–2990.Google Scholar
  11. Ghommam, J., Mehrjerdi, H., & Saad, M. (2013). Robust formation control without velocity measurement of the leader robot. Control Engineering Practice, 21, 1143–1156.CrossRefGoogle Scholar
  12. Ghommam, J., & Saad, M. (2014). Backstepping-based coop- erative and adaptive tracking control design for a group of underactuated AUVs in horizontal plan. International Journal of Control, 87(5), 1076–1093.MathSciNetCrossRefzbMATHGoogle Scholar
  13. Guo, W., Lü, J., Chen, S., & Yu, X. (2011). Second-order tracking control for leader-follower multi-agent flocking in directed graphs with switching topology. Systems and Control Letters, 60, 1051–1058.Google Scholar
  14. He, X., Wang, Q., & Yu, W. (2014). Finite-time containment control for second-order multiagent systems under directed topology. IEEE Transactions on Circuit and Systems-II, 61(8), 619–623.CrossRefGoogle Scholar
  15. Hong, Y., Gao, L., Cheng, D., & Hu, J. (2007). Lyapunov-based approach to multiagent systems with switching jointly connected interconnection. IEEE Transactions on Automatic Control, 52(5), 943–948.MathSciNetCrossRefGoogle Scholar
  16. Khoo, S., Xie, L., & Man, Z. (2009). Robust finite-time consensus tracking algorithm for multirobot systems. IEEE/ASME Transactions on Mechatronics, 14(2), 219–228.CrossRefGoogle Scholar
  17. Levant, A. (1993). Sliding order and sliding accuracy in sliding mode control. International Journal of Control, 58(6), 1247–1263.MathSciNetCrossRefzbMATHGoogle Scholar
  18. Levant, A. (2001). Universal single-input single-output (SISO) sliding-mode controllers with finite-time convergence. IEEE Transactions on Automatic Control, 46(1), 1447–1451.MathSciNetCrossRefzbMATHGoogle Scholar
  19. Levant, A. (2003). Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control, 76(9/10), 924–941.MathSciNetCrossRefzbMATHGoogle Scholar
  20. Li, T., & Zhang, J.-F. (2010). Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises. IEEE Transactions on Automatic Control, 55(9), 2043–2057.MathSciNetCrossRefGoogle Scholar
  21. Li, Z., Duan, Z., Chen, G., & Huang, L. (2010). Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint. IEEE Transactions on Circuits and Systems -I, 57(1), 213–224.MathSciNetCrossRefGoogle Scholar
  22. Lin, P., & Jia, Y. (2009). Consensus of second-order discrete-time multiagent systems with nonuniform time-delays and dynamically changing topologies. Automatica, 45(9), 2154–2158.MathSciNetCrossRefzbMATHGoogle Scholar
  23. Mehrjerdi, H., Saad, M., & Ghommam, J. (2011). Hierarchical fuzzy cooperative control and path following for a team of mobile robots. IEEE/ASME Transactions on Mechatronics, 16(5), 907–917.CrossRefGoogle Scholar
  24. Moulay, E., & Perruquetti, W. (2008). Finite time stability conditions for non autonomous continuous systems. International Journal of Control, 81(5), 797–803.MathSciNetCrossRefzbMATHGoogle Scholar
  25. Pack, D. J., DeLima, P., Toussaint, G. J., & York, G. (2009). Cooperative control of UAVs for localization of intermittently emitting mobile targets. IEEE Transactions on Systems Man and Cybernatics-Part B: 39(4), 959–970.Google Scholar
  26. Rath, J., Veluvolu, K., & Defoort, M. (2015). Simultaneous estimation of road profile and tyre road friction for automotive vehicle. IEEE Transactions on Vehicular Technology, 64(10), 4461–4471.Google Scholar
  27. Ren, W., & Beard, R. W. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), 655–661.MathSciNetCrossRefGoogle Scholar
  28. Shtessel, Y., Taleb, M., & Plestan, F. (2012). A novel adaptive-gain supertwisting sliding mode controller: Methodology and application. Automatica, 48(5), 759–769.MathSciNetCrossRefzbMATHGoogle Scholar
  29. Shtessel, Y. B., Moreno, J. A., Plestan, F., Fridman, L. M., and Poznyak, A. S. (2010). Super-twisting adaptive sliding mode control: A Lyapunov design. In 49th IEEE Conference on Decision and Control, Atlanta, USA, (pp. 5109–5113).Google Scholar
  30. Weigang, L., de Souza, B. B., Crespo, A. M. F., & Alves, D. P. (2008). Decision support system in tactical air traffic flow management for air traffic flow controllers. Journal of Air Transport Management, 14, 329–336.CrossRefGoogle Scholar
  31. Yoon, S., & Qiao, C. (2011). Cooperative search and survey using autonomous underwater vehicles (AUVs). IEEE Transactions on Parallel and Distributed Systems, 22(3), 364–379.Google Scholar
  32. Yu, S., & Long, X. (2015). Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode. Automatica, 54, 158–165.MathSciNetCrossRefzbMATHGoogle Scholar
  33. Zhang, W. & Wang, Z. (2015). Adaptive output consensus tracking of uncertain multiagent systems. International Journal of Systems Science, 46(13), 2367–2379.Google Scholar
  34. Zhao, D., Zou, T., Li, S., & Zhu, Q. (2011). Adaptive backstepping sliding mode control for leader-follower multi-agent systems. IET Control Theory and Applications, 6(8), 1109–1117.MathSciNetCrossRefGoogle Scholar
  35. Zuo, Z. (2015). Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica, 54, 305–309.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore
  2. 2.Department of Electrical EngineeringEcole de Technologie SuperieureMontrealCanada

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