Kybernetika 49 no. 4, 507-523, 2013

Finite-time cooperative tracking control for a class of second-order nonlinear multi-agent systems

Haibo Du, Yigang He and Yingying Cheng


The problem of finite-time cooperative tracking control for a class of second-order nonlinear multi-agent systems is studied in this paper. The agent dynamic is described by a second-order nonlinear system with uncertain time-varying control coefficients and unknown nonlinear perturbations. Based on the finite-time control technique and graph theory, a class of distributed finite-time control laws are proposed which are only based on the neighbors' information. Under the proposed controller, it is shown that the states of all the agents can reach consensus in a finite time and the final consensus state is the desired signal. As an application of the proposed theoretic results, the problem of distributed finite-time attitude cooperative control for the roll channels of multiple bank-to-turn (BTT) missiles is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.


multi-agent systems, nonlinear system, finite-time control, bank-to-turn missiles\!\!\!\!


93A14, 93C10, 93D15, 93D21


  1. S. Bhat and D. Bernstein: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38 (2000), 751-766.   CrossRef
  2. Y. Cao, W. Ren and Z. Meng: Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking. Syst. Control Lett. 59 (2010), 522-529.   CrossRef
  3. J. Cortes: Finite-time convergent gradient flows with applications to network consensus. Automatica 42 (2006), 1993-2000.   CrossRef
  4. D. Dimarogonas, P. Tsiotras and K. Kyriakopoulos: Leader-follower cooperative attitude control of multiple rigid bodies. Syst. Control Lett. 58 (2009), 429-435.   CrossRef
  5. D. Dimarogonas and K. Kyriakopoulos: On the rendezvous problem for multiple nonholonomic agents. IEEE Trans. Automat. Control 52 (2007), 916-922.   CrossRef
  6. S. Ding, S. Li and W. Zheng: Nonsmooth stabilization of a class of nonlinear cascaded systems. Automatica 48 (2012), 2597-2606.   CrossRef
  7. W. Dong and A. Farrell: Cooperative control of multiple nonholonomic mobile agents. IEEE Trans. Automat. Control 53 (2008), 1434-1448.   CrossRef
  8. G. Duan and H. Wang: Parameter design of smooth switching controller and application for bank-to-turn missiles. (In Chinese.) Aerospace Control 23 (2005), 41-46.   CrossRef
  9. A. Fax and R. Murray: Information flow and cooperative control of vehicle formations. IEEE Trans. Automat. Control 49 (2004), 1453-1464.   CrossRef
  10. L. Gao, Y. Tang, W. Chen and H. Zhang: Consensus seeking in multi-agent systems with an active leader and communication delays. Kybernetika 47 (2011), 773-789.   CrossRef
  11. G. Hardy, J. Littlewood and G. Polya: Inequalities. Cambridge University Press, Cambridge 1952.   CrossRef
  12. Y. Hong, L. Gao, D. Cheng and J. Hu: Lyapunov-based approach to multiagent systems with switching jointly connected interconnection. IEEE Trans. Automat. Control 52 (2007), 943-948.   CrossRef
  13. Y. Hong, J. Hu and L. Gao: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42 (2006), 1177-1182.   CrossRef
  14. Y. Hong, G. Chen and L. Bushnell: Distributed observers design for leader-following control of multi-agent networks. Automatica 44 (2008), 846-850.   CrossRef
  15. Q. Hui, W. M. Haddad and S. P. Bhat: Finite-time semistability and consensus for nonlinear dynamical networks. IEEE Trans. Automat. Control 53 (2008), 1887-1990.   CrossRef
  16. I. Jeon and J. Lee: Homing guidance law for cooperative attack of multiple missiles. J. Guid., Control Dynam. 33 (2010), 275-280.   CrossRef
  17. S. Khoo, L. Xie and Z. Man: Robust finite-time consensus tracking algorithm for multirobot systems. IEEE/ASME Trans. Mechatronics 14 (2009), 219-228.   CrossRef
  18. S. Li, H. Du and X. Lin: Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica 47 (2011), 1706-1712.   CrossRef
  19. S. Li, H. Liu and S. Ding: A speed control for a PMSM using finite-time feedback control and disturbance compensation. Trans. Inst. Measurement and Control 32 (2010), 170-187.   CrossRef
  20. S. Li, S. Ding and Q. Li: Global set stabilisation of the spacecraft attitude using finite-time control technique. Internat. J. Control 5 (2009), 822-836.   CrossRef
  21. S. Li and Y. Tian: Finite-time stability of cascaded time-varying systems. Internat. J. Control 80 (2007), 646-657.   CrossRef
  22. R. Olfati-Saber and R. Murray: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control 49 (2004), 1520-1533.   CrossRef
  23. R. Olfati-Saber: Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Trans. Automat. Control 51 (2006), 410-420.   CrossRef
  24. C. Qian and J. Li: Global finite-time stabilization by output feedback for planar systems without observable linearization. IEEE Trans. Automat. Control 50 (2005), 885-890.   CrossRef
  25. C. Qian and W. Lin: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Automat. Control 46 (2001), 1061-1079.   CrossRef
  26. W. Ren and E. Atkins: Distributed multi-vehicle coordinated control via local information exchange. Internat. J. Robust Nonlinear Control 17 (2007), 1002-1033.   CrossRef
  27. W. Ren: Distributed attitude alignment in spacecraft formation flying. Internat. J. Adapt. Control 21 (2007), 95-113.   CrossRef
  28. W. Ren: Multi-vehicle consensus with a time-varying reference state. Syst. Control Lett. 56 (2007), 474-483.   CrossRef
  29. W. Ren: On consensus algorithms for double-integrator dynamics. IEEE Trans. Automat. Control 53 (2008), 1503-1509.   CrossRef
  30. G. Shi and Y. Hong: Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies. Automatica 45 (2009), 1165-1175.   CrossRef
  31. G. Scutari, S. Barbarossa and L. Pescosolido: Distributed decision through self-synchronizing sensor networks in the presence of propagation delays and asymmetric channels. IEEE Trans. Signal Process. 56 (2008), 1667-1684.   CrossRef
  32. F. Tan and G. Duan: Global stabilizing controller design for linear time-varying systems and its application on BTT missiles. J. Systems Engrg. Electronics 19 (2008), 1178-1184.   CrossRef
  33. F. Xiao, L. Wang, J. Chen and Y. Gao: Finite-time formation control for multi-agent systems. Automatica 45 (2009), 2605-2611.   CrossRef
  34. L. Wang and F. Xiao: Finite-time consensus problems for networks of dynamic agents. IEEE Trans. Automat. Control 55 (2010), 950-955.   CrossRef
  35. X. Wang, X. Sun, S. Li and H. Ye: Finite-time position tracking control of rigid hydraulic manipulators based on high-order sliding mode. In: Proc. Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 226 (2012), pp. 394-415.   CrossRef
  36. X. Wang and Y. Hong: Finite-time consensus for multi-agent networks with second-order agent dynamics. In: Proc. 17th IFAC World Congress, Korea 2008, pp. 15185-15190.   CrossRef
  37. C. Zhang, S. Li and S. Ding: Finite-time output feedback stabilization and control for a quadrotor mini-aircraft. Kybernetika 48 (2012), 206-222.   CrossRef