Adaptive Output Feedback Boundary Stabilization for First-order Hyperbolic Distributed Parameter Systems

This paper investigates the adaptive output feedback boundary stabilization problem for a type of first-order hyperbolic distributed parameter systems with an unknown spatially varying parameter. To estimate the system state, two filters are introduced and an observer is constructed by the two filters. Then based on the observer, a kernel function is introduced and the backstepping control law is designed. Moreover, the parameter updating law is designed by the Lyapnouv approach to deal with the spatially varying parameter. It is proved that the whole closed-loop system is L₂ stable. The efficiency of the adaptive controller is verified by simulation results.