Adaptive stabilization for a class of coupled PDE-ODE systems with multiple unknown parameters

This paper investigates the adaptive stabilization for a class of coupled PDE-ODE systems with multiple unknown parameters. The systems under investigation are more general and representative, due to the presence of multiple unknown parameters and coupling between the sub-systems which makes the conventional methods on this topic ineffective. Motivated by the existing results, a reversible infinite-dimensional backstepping transformation with new kernel functions is first introduced to change the original system into a target system, which makes the control design and performance analysis of the original system 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.