Abstract
In this paper, we are concerned with output feedback stabilization for a one-dimensional anti-stable wave equation with disturbance. First, we design a disturbance estimator for the original system. Then, we propose an output feedback controller for the original system. By calculation, the closed-loop of original system is proved to be exponentially stable and well-posed. Finally, this paper is summarized.
Highlights
The wave equation is a set of differential equations derived from Maxwell’s equations, which describes the wave characteristics of electromagnetic field
Anti-stable one-dimensional wave equation with boundary disturbance has been researched in different ways in the field of control
There are many kinds of disturbances, the “backstepping” method for the problem of stabilization of one-dimensional wave equation with input harmonic disturbance is adopted in the design of the adaptive regulator in Guo [12] (2013)
Summary
The wave equation is a set of differential equations derived from Maxwell’s equations, which describes the wave characteristics of electromagnetic field. Anti-stable one-dimensional wave equation with boundary disturbance has been researched in different ways in the field of control. On this issue, there is used the Lyapunov function approach to design controller in Guo [1] (2014). A class of nonlinear systems is dealt with a modified nonlinear extended state observer (ESO) of a time-varying gain in active disturbance rejection control (ADRC) in Zhao [2] (2015). There are many kinds of disturbances, the “backstepping” method for the problem of stabilization of one-dimensional wave equation with input harmonic disturbance is adopted in the design of the adaptive regulator in Guo [12] (2013). There are many design methods for a boundary controlled one-dimensional wave equation with external disturbance.
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