Asymptotic stabilization for uncertain coupled PDE-ODE systems

The adaptive stabilization is investigated for a class of coupled PDE-ODE systems with parametric uncertainties. The presence of the uncertainties makes the system under investigation essentially different from that of the related literature, and moreover it results in the incapability of the methods in the literature. Motivated by the existing works, an infinite-dimensional backstepping transformation is first introduced to transform the original system into a pivotal target system which makes the control design and performance analysis much convenient. Then, by utilizing Lyapunov method and some adaptive techniques, an adaptive stabilizing controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converging to zero.