Adaptive Output-Feedback Stabilization for PDE-ODE Cascaded Systems with Unknown Control Coefficient

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This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cas-caded systems.Remarkably,the PDE subsystem allows unknown control coefficient and spatially varying parameter,and only its one boundary value is measurable.This renders the system in ques-tion more general and practical,and the control problem more challenging.To solve the problem,an invertible transformation is first introduced to change the system into an observer canonical form,from which a couple of filters are constructed to estimate the unmeasurable states.Then,by adaptive technique and infinite-dimensional backstepping method,an adaptive controller is constructed which guarantees that all states of the resulting closed-loop system are bounded while the original system states converging to zero.Finally,a numerical simulation is provided to illustrate the effectiveness of the proposed method.
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