Adaptive stabilization for a class of coupled parabolic PDEs with unknown constant coefficients

This paper investigates the adaptive stabilization for a class of coupled parabolic PDEs. The problem remains unsolved since the presence of unknown parameters make the existing methods for coupled parabolic PDEs ineffective. By skillfully combining Lyapunov method and infinite-dimensional backstepping method, an adaptive state-feedback controller is designed to ensure that all the closed-loop system states are bounded while the original system states converging to zero. It is worth pointing out that, the coupling between subsystems makes the control design and stability analysis more difficult than those of the related literature.