Stabilization of One-Dimensional Wave Equation With Nonlinear Boundary Condition Subject to Boundary Control Matched Disturbance

In this paper, we consider the stabilization of a one-dimensional wave equation with nonlinear van der Pol type boundary condition that covers the antistable boundary, and subject to boundary control matched disturbance on the other side. Due to the nonlinear boundary condition and disturbance, the...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2019-07, Vol.64 (7), p.3068-3073
Main Authors: Liu, Jun-Jun, Wang, Jun-Min
Format: Article
Language:English
Subjects:
Bifurcation
Bifurcations
Boundary conditions
Boundary control
Chaos theory
Closed loop systems
Computer simulation
Feedback control
Mathematical model
Nonlinear van der Pol type boundary
Numerical simulation
Propagation
Sliding mode control
sliding mode control (SMC)
Stabilization
wave equation
Wave equations
Well posed problems
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Summary:In this paper, we consider the stabilization of a one-dimensional wave equation with nonlinear van der Pol type boundary condition that covers the antistable boundary, and subject to boundary control matched disturbance on the other side. Due to the nonlinear boundary condition and disturbance, the uncontrolled system may present spatiotemporal chaotic, period-doubling bifurcation, and some other dynamical behaviors. We will deal with this disturbance, which is supposed to be bounded only, by the integral sliding mode control. The well-posedness of the system for the closed-loop system is proved and the "reaching condition" is obtained. Finally, we provide some numerical simulations to illustrate the theoretical outcomes.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2874746