Adaptive output-feedback stabilization of linear 2×2 hyperbolic systems using anti-collocated sensing and control

We construct a control law that manages to adaptively stabilize a class of linear 2×2 hyperbolic systems of partial differential equations (PDEs) from a single boundary sensing anti-collocated with the boundary where actuation takes place. We do this by introducing a series of invertible transformations that bring the system into an observer canonical form, for which adaptive control design becomes feasible. We establish pointwise boundedness of all signals in the closed loop system, and pointwise convergence of the system states to zero. The theory is demonstrated in a simulation.