Title: Output feedback exponential stabilization of a nonlinear 1-D wave equation with boundary input,
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.