Adaptive stabilization of n+1 coupled linear hyperbolic systems with uncertain boundary parameters using boundary sensing

We design an adaptive control law stabilizing a class of systems of the form of n+1 linear partial differential equations (PDEs) of the hyperbolic type from boundary sensing only. We do this by combining a recently derived observer based on swapping design, with a backstepping-based adaptive control law with time-varying gains. Boundedness of all signals in the closed loop system and asymptotic convergence to zero pointwise in space for the system states are proved. The theory is demonstrated in a simulation.