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Adaptive output-feedback control of uncertain PDE-ODE cascade systems

This paper is devoted to the adaptive output-feedback control of the uncertain hybrid PDE-ODE systems. To estimate the unmeasured states of the considered system, an observer is first given, and based on which we construct the desired adaptive controller successfully by using the backstepping technique. Next, by semigroup theory, we establish the well-posedness of the entire closed-loop system. At last, to analyze the stability of the entire closed-loop system, by LaSalle's invariance principle, we prove the asymptotic stability of the system, and moreover, we show that the estimates of all unknown parameters converge to their own real values ultimately.