The adaptive stabilization is investigated for a class of coupled PDE-ODE systems with
multiple uncertainties. The presence of the multiple uncertainties and the interaction
between the sub-systems makes the systems to be considered more general and
representative, and moreover it may result in the ineffectiveness of the conventional
methods on this topic. Motivated by the existing literature, an infinite-dimensional
backsteppping transformation with new kernel functions is first introduced to change the
original system into a target system, from which the control design and performance
analysis of the original system will become quite convenient. Then, by certainty
equivalence principle and Lyapunov method, 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. A simulation example is
provided to validate the proposed method.