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arXiv · 1706.02152

Output feedback exponential stabilization of a nonlinear 1-D wave equation with boundary input

Hua-Cheng Zhou·George Weiss
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Abstract

This paper develops systematically the output feedback exponential stabilization for a one-dimensional unstable/anti-stable wave equation where the control boundary suffers from both internal nonlinear uncertainty and external disturbance. Using only two displacement signals, we propose a disturbance estimator that not only can estimate successfully the disturbance in the sense that the error is in $L^2(0,\infty)$ but also is free high-gain. With the estimated disturbance, we design a state observer that is exponentially convergent to the state of original system. An observer-based output feedback stabilizing control law is proposed. The disturbance is then canceled in the feedback loop by its approximated value. The closed-loop system is shown to be exponentially stable and it can be guaranteed that all internal signals are uniformly bounded.

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Hua-Cheng Zhou, George Weiss. 2017-06-07. Output feedback exponential stabilization of a nonlinear 1-D wave equation with boundary input. https://arxiv.org/abs/1706.02152

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