Backstepping boundary control for first-order hyperbolic PDEs with unknown spatially varying parameter

The adaptive boundary stabilization is investigated for a class of systems described by first-order hyperbolic PDEs with unknown spatially varying parameter. Towards the system unknowns, a dynamic compensation is first given by using infinite-dimensional backstepping method, adaptive techniques and projection operator. Then an adaptive boundary controller is constructed by certainty equivalence principle, which can stabilize the original system in a certain sense.