Output feedback control for wave equations with nonlinear boundary condition and disturbance inputs
The output feedback control of infinite dimensional systems is an important research topic in control theory.Compared with linear boundary input,nonlinear boundary conditions are more applied to practical mathematical models,which can cause various dynamic behaviors,such as chaotic acoustic vibration,period-doubling bifurcation,square wave,and so on.In this paper,the output feedback stability problem of one dimensional wave equation with nonlinear displace-ment boundary condition at left end and total disturbance input at right end is studied.Firstly,the well-posedness of open loop systems is proved by using operator semigroup theory.Secondly,due to the existence of internal nonlinear terms and external disturbances,we prove that the estimator can estimate total disturbances by constructing an infinite-dimensional disturbance estimator.Then,the state observer is designed by means of the measured output signal of the original system,and the stability controller is constructed and the closed-loop system is obtained.Finally,the well-posedness and asymptotic stability of the closed-loop system are proved.
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