Kybernetika 48 no. 6, 1180-1193, 2012

Finite-time consensus problem for multiple non-holonomic mobile agents

Jiankui Wang, Zhihui Qiu and Guoshan Zhang


In this paper, the problem of finite time consensus is discussed for multiple non-holonomic mobile agents. The objective is to design a distributed finite time control law such that the controlled multiple non-holonomic mobile agents can reach consensus within any given finite settling time. We propose a novel switching control strategy with the help of time-rescalling technique and graph theory. The numerical simulations are presented to show the effectiveness of the method.


finite time consensus, nonholonomic system, time-rescaling, mobile agents


93D15, 93D21


  1. S. P. Bhat and D. S. Bernstein: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Automat. Control 43 (1998), 5, 678-682.   CrossRef
  2. S. P. Bhat and D. S. Bernstein: Geometric homogeneity with applications to finite-time stability. Math. Control, Signals, and Systems 17 (2005), 2, 101-127.   CrossRef
  3. W. J. Dong and J. A. Farrell: Cooperative control of multiple nonholonomic mobile agents. IEEE Trans. Automat. Control 53 (2008), 6, 1434-1448.   CrossRef
  4. H. Du, S. Li and C. Qian: Finite-time attitude tracking control of spacecraft with application to attitude synchronization. IEEE Trans. Automat. Control 56 (2011), 11, 2711-2717.   CrossRef
  5. H. Du, S. Li and X. Lin: Finite-time formation control of multi-agent systems via dynamic output feedback. Internat. J. Robust and Nonlinear Control (2012), published online.   CrossRef
  6. X. Feng and W. Long: Reaching agreement in finite time via continuous local state feedback. In: Chinese Control Conference 2007, pp. 711-715.   CrossRef
  7. Y. Hong and J. Wang: Stabilization of uncertain chained form systems within finite settling time. IEEE Trans. Automat. Control 50 (2005), 9, 1379-1384.   CrossRef
  8. Y. Hong, J. P. Hu and L. X. Gao: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42 (2006), 7, 1177-1182.   CrossRef
  9. Y. Hong, Z. Jiang and G. Feng: Finite-time input-to-state stability and applications to finite-time control design. SIAM J. Control Optim. 48 (2010), 7, 4395-4418.   CrossRef
  10. E. W. Justh and P. S. Krishnaprasad: Equilibrium and steering laws for planar formations. Systems Control Lett. 52 (2004), 1, 25-38.   CrossRef
  11. R. W. Beard, J. Lawton and B. J. Young: A decentralized approach to formation maneuvers. IEEE Trans. Robotics Automat. 19 (2003), 6, 933-941.   CrossRef
  12. 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), 2, 170-187.   CrossRef
  13. S. Li, H. Du and X. Lin: Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica 47 (2011), 8, 1706-1712.   CrossRef
  14. R. Olfati-Saber and R. M. Murray: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control 49 (2004), 9, 1520-1533.   CrossRef
  15. J. Wang, G. Zhang and H. Li: Adaptive control of uncertain nonholonomic systems in finite time. Kybernetika 45 (2009), 5, 809-824.   CrossRef
  16. J. Wang, Y. Zhao, X. Song and G. Zhang: Semi-global robust finite time stabilization of non-holonomic chained form systems with perturbed terms. In: 8th World Congress on Intelligent Control and Automation (WCICA) 2010, pp. 3662-3667.   CrossRef
  17. X. L. Wang and Y. Hong: Finite-time consensus for multi-agent networks with second-order agent dynamics. In: Proc. 17th World Congress The International Federation of Automatic Control (2008), pp. 15185-15190.   CrossRef