Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 596-610.

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Exponential Tracking Control for a Star-Shaped Network of Euler-Bernoulli Beams with Unknown Internal Disturbance

Yaxuan Zhang1,*(),Genqi Xu2,Yanni Guo1   

  1. 1 Department of Mathematics, College of Science, Civil Aviation University of China, Tianjin 300300
    2 College of Mathematics, Tianjin University, Tianjin 300350
  • Received:2017-05-27 Online:2019-06-26 Published:2019-06-27
  • Contact: Yaxuan Zhang
  • Supported by:
    the NSFC(61503385);the NSFC(11705279);the Fundamental Research Funds for the Central Universities(3122018L004);the Scientific Research Project of Tianjin Municipal Education Commission(2018KJ253)


In this paper, the exponential tracking control for a star-shaped network of Eulerbernoulli beams with unknown internal disturbance is studied. The problem is transformed into the stabilization of the error system between the objective network and the active network. The idea of sliding-mode control is used to design a nonlinear feedback control law. The solvability of the error system is obtained via monotone operator theory under an appropriately chosen space norm. The error system is proved to be exponentially stabilized at any decay rate by a suitable Lyapunov functional. So the objective network can track the active network exponentially at any designated rate.

Key words: Tracking control, Unknown internal disturbance, Star-shaped network of Eulerbernoulli beams, Sliding-mode control, Exponential stabilization

CLC Number: 

  • O231.9