Adaptive boundary stabilization 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 controller is constructed by certainty equivalence principle, which can stabilize the original system in a certain sense. Moreover, the effectiveness of the proposed method is illustrated by a simulation example. Copyright (C) 2015 John Wiley & Sons, Ltd.