Mohammadali Ghadiri-Modarres - Department of Electrical Engineering, Arak University of Technology, Arak, Iran
Elham Aarabi - Dept. of Electr. and Comp. Eng., Isfahan University of Technology, Isfahan ۸۴۱۵۶-۸۳۱۱۱, Iran
Mohsen Mojiri - Dept. of Electr. and Comp. Eng., Isfahan University of Technology, Isfahan ۸۴۱۵۶-۸۳۱۱۱, Iran

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.

Adaptive control, partial differential equation, backstepping