Adaptive Boundary Stabilization of the Heat PDE with an Intermediate Point Non-local Term

This paper develops an adaptive state-feedback control design scheme for boundary stabilization of theheat partial differential equation (PDE) containing a destabilizing non-local term with unknown coefficientat its interior point. To this end, the underlying non-adaptive backstepping-forwarding transformation andthe control law are modified by replacing the unknown parameter by its adaptive estimate and the Lyapunovbased update law is developed for the adaptive stabilization. The closed-loop stability and the regulation ofthe plant state are shown and the effectiveness of the proposed controller is verified through a numericalsimulation example.

Keywords:

Adaptive control , partial differential equation , backstepping