Adaptive control of linear 2×2 hyperbolic systems

We design two closely related state feedback adaptive control laws for stabilization of a class of 2×2 linear hyperbolic system of partial differential equations (PDEs) with constant but uncertain in-domain and boundary parameters. One control law uses an identifier, while the other is based on swapping design. We establish boundedness of all signals in the closed loop system, pointwise in space and time, and convergence of the system states to zero pointwise in space. The theory is demonstrated in simulations.