SCIENCE CHINA Information Sciences, Volume 59, Issue 9: 092206(2016) https://doi.org/10.1007/s11432-016-5554-4

Feedback control for a class of second order hyperbolic distributed parameter systems

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  • ReceivedJun 14, 2015
  • AcceptedSep 30, 2015
  • PublishedAug 23, 2016


This paper deals with the problem of state feedback control for a class of {the} distributed parameter systems with {the} disturbance term. {And} the considered distributed parameter systems are composed of {the} second order hyperbolic partial differential equations. Two different classes of restrictions on the disturbance term are given, one is that the disturbance term satisfies the linear growth constraint condition to the state variables of the system, and the other is that the disturbance term obeys the bound constraint under the significance of $L_2 $. Based on {a} variable structure method, the state feedback controllers are obtained by means of constructing appropriate Lyapunov functional. The closed-loop systems are globally asymptotically stable on $W^{1,2}(0,1)\times L_2 (0,1)$ space under the effect of the state feedback control laws. Simulation results illustrate the effectiveness of the proposed method.

Funded by

National Natural Science Foundation of China(11371013)



This work was supported by National Natural Science Foundation of China (Grant No. 11371013).


[1] Smyshlyaev A, Krstic M. Boundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundary. Syst Control Lett, 2009, 58: 617-623 CrossRef Google Scholar

[2] Smyshlyaev A, Krstic M. Backstepping observers for a class of parabolic PDEs. Syst Control Lett, 2005, 54: 613-625 CrossRef Google Scholar

[3] Krstic M, Smyshlyaev A. Adaptive control of PDEs. Ann Rev Control, 2008, 32: 149-160 CrossRef Google Scholar

[4] Cheng M B, Radisavljevic V, Su W C. Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties. Automatica, 2011, 47: 381-387 CrossRef Google Scholar

[5] Orlov Y. Discontinuous unit feedback control of uncertain infinite-dimensional systems. IEEE Trans Autom Control, 2000, 45: 834-843 CrossRef Google Scholar

[6] Fu Q. Iterative learning control for second order nonlinear hyperbolic distributed parameter systems (in Chinese). J Syst Sci Math Sci, 2014, 34: 284-293 Google Scholar

[7] Orlov Y, Pisano A, Usai E. Continuous state-feedback tracking of the uncertain heat diffusion process. Syst Control Lett, 2010, 59: 754-759 CrossRef Google Scholar

[8] Orlov Y, Pisano A, Usai E. Exponential stabilization of the uncertain wave equation via distributed dynamic input extension. IEEE Trans Autom Control, 2011, 56: 212-217 CrossRef Google Scholar

[9] Pisano A, Orlov Y, Usai E. Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques. SIAM J Control Optim, 2011, 49: 363-382 CrossRef Google Scholar

[10] Orlov Y. Discontinuous Systems Lyapunov Analysis and Robust Synthesis Under Uncertainty Conditions. Berlin: Springer-Verlag, 2009. Google Scholar

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