Finite-Time Consensus for Systems with Second-Order Uncertain Dynamics Under Directed Topology

  • Yongduan SongEmail author
  • Yujuan Wang
Part of the Communications and Control Engineering book series (CCE)


In Chap. 7, we have explicitly addressed the finite-time leaderless consensus control problem of nonlinear MAS with second-order dynamics in the presence of unknown time-varying gain and non-parametric uncertainties under the local and undirected communication condition. By considering that in most practical applications, the networked communication among the subsystems is not only local but also not bidirectional, and it is highly desirable to consider the local and one-way directed communication condition. For agents with second-order dynamics in the presence of non-parametric uncertainties under local and one-way directed communication topology, the finite-time leaderless consensus control problem is interesting and also challenging, worthy of further studying. Compared with the control results derived in Chap. 7, the finite-time leaderless consensus of second-order nonlinear MAS with non-parametric uncertainties under one-way directed communication topology is much more challenging, where the one-way directed communication topology obviously complicates the underlying problem significantly. This is mainly because the symmetric property does not hold for the directed Laplacian, which imposes a significant technique challenge to extend the existing finite-time adaptive consensus control methods derived from undirected graph to directed graph. In this chapter, we attempt to provide a solution to this problem under directed graph topology.


  1. 1.
    Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43(5), 678–682 (1998)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Qian, C., Lin, W.: Non-Lipschitz continuous stabilizer for nonlinear systems with uncontrollable unstable linearization. Syst. Control Lett. 42(3), 185–200 (2001)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hardy, G., Littlewood, J., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1952)zbMATHGoogle Scholar
  4. 4.
    Wang, Y.J., Song, Y.D., Krstic, M., Wen, C.Y.: Fault-tolerant finite time consensus for multiple uncertain nonlinear mechanical systems under single-way directed communication interactions and actuation failures. Automatica 63, 374–383 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zhang, H., Lewis, F.L., Qu, Z.: Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs. IEEE Trans. Ind. Electron. 59, 3026–3041 (2012)CrossRefGoogle Scholar
  6. 6.
    Polycarpout, M.M., Ioannout, P.A.: A robust adaptive nonllinear control design. In: American Control Conference, pp. 1365–1369 (1993)Google Scholar
  7. 7.
    Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Almeida, J., Silvestre, C., Pascoal, A.M.: Cooperative control of multiple surface vessels with discrete-time periodic communications. Int. J. Robust. Nonlinear Control 22(4), 398–419 (2012)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of AutomationChongqing UniversityChongqingChina

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