Adaptive stabilization of coupled PDE–ODE systems with multiple uncertainties

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