Stabilization of a linear 2 × 2 hyperbolic system with an uncertain boundary parameter from collocated sensing and control

We establish a control law that manages to adaptively stabilize a system of 2 × 2 linear hyperbolic partial differential equations (PDEs) from sensing and control anti-collocated with an uncertain boundary parameter. We do this by combining a recently derived adaptive observer with a backstepping-based control law, and prove closed loop stability in the L
₂
-sense. The theory is demonstrated in a simulation.