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Time-varying Formation Tracking for Second-order Multi-agent Systems Subjected to Switching Topology and Input Saturation

  • Jing Liu
  • Jian-an FangEmail author
  • Zhen Li
  • Guang He
Article
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Abstract

This paper addresses the problem of time-varying formation tracking for a kind of second-order multi-agent systems with a switching topology, in which the dynamics of agents are modeled by double integrators and harmonic oscillators respectively. The control input of each agent is subject to saturation. First, depending on the low-gain state feedback technique, an algorithm is designed to solve semi-global time-varying formation tracking problem, where feasibility condition of formation tracking is introduced. Then, by utilizing the Lyapunov function and low-gain feedback theory, it is proved that second-order multi-agent system with a switching topology achieves the specified semi-global time-varying formation tracking if some sufficient conditions hold. Further, as an extension, jointly connected switching topology is considered, and the corresponding formation tracking problem is also explored. Subsequently, several simulation examples is worked out for illustration.

Keywords

Formation tracking control input saturation second-order multi-agent systems switching topology 

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References

  1. [1]
    R. Olfati-Saber, J. Fax, and R. Murray, “Consensus and cooperation in networked multi-agent systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 215–233, 2007.zbMATHCrossRefGoogle Scholar
  2. [2]
    N. Nigam, S. Bieniawski, I. Kroo, and J. Vian, “Control of multiple uavs for persistent surveillance: Algorithm and flight test results,” IEEE Transactions on Control Systems Technology, vol. 20, no. 5, pp. 1236–1251, September 2012.CrossRefGoogle Scholar
  3. [3]
    Y. Tang, H. Gao, J. Lu, and J. Kurths, “Pinning distributed synchronization of stochastic dynamical networks: a mixed optimization approach,” IEEE Trans Neural Netw Learn Syst, vol. 25, no. 10, pp. 1804–1815, October 2014.CrossRefGoogle Scholar
  4. [4]
    J. Fu, G. Wen, and W. Yu, “Consensus of second-order multiagent systems with both velocity and input constraints,” IEEE Transactions on Industrial Electronics, vol. 66, no. 10, pp. 7946–7955, October 2019.CrossRefGoogle Scholar
  5. [5]
    D. Zheng, H. Zhang, and J. Andrew, “Consensus of the second-order multi-agent systems under asynchronous switching with a controller fault,” International Journal of Control, Automation and Systems, vol. 17, no. 1, pp. 136–144, January 2019.CrossRefGoogle Scholar
  6. [6]
    Y. Tang, Q. Feng, H. Gao, and J. Kurths, “Synchronization in complex networks and its application c a survey of recent advances and challenges,” Annual Reviews in Control, vol. 38, no. 2, pp. 184–198, 2014.CrossRefGoogle Scholar
  7. [7]
    W. Zhang, Z. D. Wang, and Y. Liu, “Sampled-data consensus of nonlinear multiagent systems subject to cyber attacks,” International Journal of Robust and Nonlinear Control, vol. 28, no. 1, pp. 53–67, January 2018.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    X. Wu, Y. Tang, J. Cao, and X. Mao, “Stability analysis for continuous-time switched systems with stochastic switching signals,” IEEE Transactions on Automatic Control, vol. 63, no. 3, pp. 3083–3090, September 2018.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    J. Qin, W. Zheng, H. Gao, Q. Ma, and W. Fu, “Containment control for second-order multiagent systems communicating over heterogeneous networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 9, pp. 2143–2155, September 2017.MathSciNetGoogle Scholar
  10. [10]
    J. Wang and H. Wu, “Leader-following formation control of multi-agent systems under fixed and switching topologies,” IEEE International Journal of Control, vol. 85, no. 6, pp. 695–705, 2012.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Y. Tang, X. Xing, H. Karimi, L. Kocarev, and J. Kurths, “Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses,” IEEE Transactions on Industrial Electronics, vol. 63, no. 2, pp. 1299–1307, March 2016.CrossRefGoogle Scholar
  12. [12]
    H. Shen, Y. Wang, J. Xia, J. Park, and Z. Wang, “Faulttolerant leader-following consensus for multi-agent systems subject to semi-Markov switching topologies: An event-triggered control scheme,” Nonlinear Analysis: Hybrid Systems, vol. 34, pp. 92–107, 2019.MathSciNetGoogle Scholar
  13. [13]
    H. Zhang, J. Park, D. Yue, and X. Xie, “Finite-horizon optimal consensus control for unknown multiagent state-delay systems,” IEEE Transactions on Cybernetics, 2018. DOI:  https://doi.org/10.1109/TCYB.2018.2856510
  14. [14]
    S. Zhu, D. Wang, and C. Low, “Cooperative control of multiple uavs for source seeking,” Journal of Intelligent & Robotic Systems, vol. 70, no. 1, pp. 293–301, April 2013.CrossRefGoogle Scholar
  15. [15]
    Y. Cao, D. Stuart, W. Ren, and Z. Meng, “Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: algorithms and experiments,” IEEE Transactions on Control Systems Technology, vol. 19, no. 4, pp. 929–938, July 2011.CrossRefGoogle Scholar
  16. [16]
    A. Loria, J. Dasdemir, and N. Jarquin, “Leader-follower formation and tracking control of mobile robots along straight paths,” IEEE Transactions on Control Systems Technology, vol. 24, no. 2, pp. 727–732, March 2016.CrossRefGoogle Scholar
  17. [17]
    S. Yoo and T. Kim, “Distributed formation tracking of networked mobile robots under unknown slippage effects,” Automatica, vol. 54, pp. 100–106, April 2015.MathSciNetzbMATHCrossRefGoogle Scholar
  18. [18]
    W. Wang, J. Huang, C. Wen, and H. Fan, “Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots,” Automatica, vol. 50, no. 4, pp. 1254–1263, April 2014.MathSciNetzbMATHCrossRefGoogle Scholar
  19. [19]
    Y. Hua, X. Dong, Q. Li, and R. Zhang, “Distributed time-varying formation robust tracking for general linear multiagent systems with parameter uncertainties and external disturbances,” IEEE Transactions on Cybernetics, vol. 47, no. 8, pp. 1959–1969, August 2017.CrossRefGoogle Scholar
  20. [20]
    J. Yu, X. Dong, Q. Li, and Z. Ren, “Practical time-varying formation tracking for second-order nonlinear multiagent systems with multiple leaders using adaptive neural networks,” IEEE Transactions on Neural Networks & Learning Systems, vol. 29, no. 12, pp. 6015–6025, December 2018.MathSciNetCrossRefGoogle Scholar
  21. [21]
    X. Dong, Y. Zhou, Z. Ren, and Y. Zhong, “Time-varying formation tracking for second-order multi-agent systems subjected to switching topologies with application to quadrotor formation flying,” IEEE Transactions on Industrial Electronics, vol. 64, no. 6, pp. 5014–5024, July 2017.CrossRefGoogle Scholar
  22. [22]
    J. Yu, X. Dong, Q. Li, and Z. Ren, “Time-varying formation tracking for high-order multi-agent systems with switching topologies and a leader of bounded unknown input,” Journal of the Franklin Institute, vol. 355, no. 5, pp. 2808–2825, March 2018.MathSciNetzbMATHCrossRefGoogle Scholar
  23. [23]
    Z. Lin, Low Gain Feedback, Springer London, 1999.Google Scholar
  24. [24]
    Q. Song, F. Liu, H. Su, and A. Vasilakos, “Semi-global and global containment control of multi-agent systems with second-order dynamics and input saturation,” International Journal of Robust & Nonlinear Control, vol. 26, no. 16, pp. 3460–3480, November 2016.MathSciNetzbMATHCrossRefGoogle Scholar
  25. [25]
    H. Su, M. Chen, J. Lam, and Z. Lin, “Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback,” IEEE Transactions on Circuits & Systems I Regular Papers, vol. 60, no. 7, pp. 1881–1889, July 2013.MathSciNetCrossRefGoogle Scholar
  26. [26]
    Q. Wang, C. Yu, and H. Gao, “Synchronization of identical linear dynamic systems subject to input saturation,” Systems & Control Letters, vol. 64, no. 64, pp. 107–113, February 2014.MathSciNetzbMATHCrossRefGoogle Scholar
  27. [27]
    L. Ding, W. Zheng, and G. Guo, “Network-based practical set consensus of multi-agent systems subject to input saturation,” Automatica, vol. 89, no. 3, pp. 316–324, March 2018.MathSciNetzbMATHCrossRefGoogle Scholar
  28. [28]
    X. Wang, H. Su, X. Wang, and G. Chen, “Fully distributed event-triggered semiglobal consensus of multi-agent systems with input saturation,” IEEE Transactions on Industrial Electronics, vol. 64, no. 6, pp. 5055–5064, July 2017.CrossRefGoogle Scholar
  29. [29]
    J. Qin, W. Fu, W. Zheng, and H. Gao, “On the bipartite consensus for generic linear multiagent systems with input saturation,” IEEE Transactions on Cybernetics, vol. 47, no. 8, pp. 1948–1958, August 2017.CrossRefGoogle Scholar
  30. [30]
    X. Zhang and X. Liu, “Consensus tracking of second order multi-agent systems with disturbances under heterogenous position and velocity topologies,” International Journal of Control, Automation and Systems, vol. 16, no. 5, pp. 2334–2342, October 2018.CrossRefGoogle Scholar
  31. [31]
    J. Liu, Y. Gu, X. Xie, D. Yue, and J. Park, “Hybrid-driven-based H∞ control for networked cascade control systems with actuator saturations and stochastic cyber attacks,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018. DOI:  https://doi.org/10.1109/TSMC.2018.2875484 CrossRefGoogle Scholar
  32. [32]
    Y. Li, J. Xiang, and W. Wei, “Consensus problems for linear time-invariant multi-agent systems with saturation constraints,” IET Control Theory & Applications, vol. 5, no. 6, pp. 823–829, April 2011.MathSciNetCrossRefGoogle Scholar
  33. [33]
    G. Xia, C. Sun, and B. Zhao, “Cooperative control of multiple dynamic positioning vessels with input saturation based on finite-time disturbance observer,” International Journal of Control, Automation and Systems, vol. 17, no. 2, pp. 370–379, February 2019.CrossRefGoogle Scholar
  34. [34]
    J. Yu, X. Dong, Q. Li, and Z. Ren, “Time-varying formation tracking control for multi-agent systems with input saturation,” Proc. of 36th Chinese Control Conference (CCC), pp. 8737–8742, July 2017.Google Scholar
  35. [35]
    X. Dong, Y. Zhou, Z. Ren, and Y. Zhong, “Time-varying formation control for unmanned aerial vehicles with switching interaction topologies,” Control Engineering Practice, vol. 46, pp. 26–36, January 2016.CrossRefGoogle Scholar
  36. [36]
    Z. Lin, L. Wang, Z. Han, and M. Fu, “Distributed formation control of multi-agent systems using complex laplacian,” IEEE Transactions on Automatic Control, vol. 59, no. 7, pp. 1765–1777, July 2014.MathSciNetzbMATHCrossRefGoogle Scholar
  37. [37]
    R. Wei and N. Sorensen, “Distributed coordination architecture for multi-robot formation control,” Robotics & Autonomous Systems, vol. 56, no. 4, pp. 324–333, April 2008.zbMATHCrossRefGoogle Scholar
  38. [38]
    G. Wen, Y. Yu, Z. Peng, and A. Rahmani, “Consensus tracking for second-order nonlinear multi-agent systems with switching topologies and a time-varying reference state,” International Journal of Control, vol. 89, no. 10, pp. 2096–2106, 2016.MathSciNetzbMATHCrossRefGoogle Scholar
  39. [39]
    Z. H. Guan, F. Sun, Y. Wang, and T. Li, “Finite-time consensus for leader-following second-order multi-agent networks,” IEEE Transactions on Circuits & Systems I Regular Papers, vol. 59, no. 11, pp. 2646–2654, November 2012.MathSciNetCrossRefGoogle Scholar
  40. [40]
    C. Godsil, G. Royle, and C. Godsil, Algebraic Graph Theory, Springer, New York, NY, USA, vol. 207, 2001.zbMATHCrossRefGoogle Scholar
  41. [41]
    X. Ge and Q. Han, “Distributed formation control of networked multi-agent systems using a dynamic event-triggered communication mechanism,” IEEE Transactions on Industrial Electronics, vol. 64, no. 10, pp. 8118–8127, October 2017.CrossRefGoogle Scholar
  42. [42]
    W. Ni, P. Zhao, X. Wang, and J. Wang, “Event-triggered control of linear systems with saturated inputs,” Asian Journal of Control, vol. 17, no. 4, pp. 1196–1208, July 2015.MathSciNetzbMATHCrossRefGoogle Scholar
  43. [43]
    Y. Hong, J. Hu, and L. Gao, “Tracking control for multiagent consensus with an active leader and variable topology,” Automatica, vol. 42, no. 7, pp. 1177–1182, July 2006.MathSciNetzbMATHCrossRefGoogle Scholar
  44. [44]
    H. Su, G. Chen, X. Wang, and Z. Lin, “Adaptive second-order consensus of networked mobile agents with nonlinear dynamics,” Automatica, vol. 47, no. 2, pp. 368–375, February 2011.MathSciNetzbMATHCrossRefGoogle Scholar
  45. [45]
    A. Langville and W. Stewart, “The kronecker product and stochastic automata networks,” Journal of Computational & Applied Mathematics, vol. 167, no. 2, pp. 429–447, July 2004.MathSciNetzbMATHCrossRefGoogle Scholar
  46. [46]
    F. Callier and C. Desoer, Linear System Theory, Springer-Verlag, 1991.Google Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.College of Information Science and TechnologyDonghua UniversityShanghaiChina
  2. 2.School of AutomationXi-an University of Posts & TelecommunicationsXi-an, ShannxiChina
  3. 3.Department of MathematicsAnhui Polytechnic UniversityWuhu, AnhuiChina

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