Advertisement

Finite-Time Leaderless Consensus Control for Systems with First-Order Uncertain Dynamics

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

Abstract

This chapter investigates the problem of finite-time leaderless consensus of networked multi-agent systems with first-order uncertain dynamics under local communication topology condition. Finite-time convergence behavior is of special importance in cooperative control of MAS, but the vast majority research on finite-time control of MAS has been focused on linear systems or nonlinear systems with nonlinearities that can be linearly parameterized, that is, the nonlinearities in that systems are assumed to exhibit the linear parametric property. The control results on finite-time distributed control of nonlinear MAS with unknown non-parametric and non-vanishing uncertainties are scarce. Extending the existing finite-time control methods for linear systems or nonlinear systems with linearly parameterized nonlinearities to MAS subject to non-parametric and non-vanishing uncertainties encounters significant technical challenge. The main hindrance stems from the fact that, in the presence of the non-parametric uncertainties, the commonly used adaptive control law cannot be used to derive the finite-time convergence because it can not ensure an important relation that is crucial to derive the finite-time convergence result.

References

  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.
    Polycarpout, M.M., Ioannout, P.A.: A robust adaptive nonlinear control design. In: American Control Conference, pp. 1365–1369 (1993)Google Scholar
  6. 6.
    Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)MathSciNetCrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Qu, Z.: Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. Springer, London (2009)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of AutomationChongqing UniversityChongqingChina

Personalised recommendations