Adaptive stabilization of a system of n + 1 coupled linear hyperbolic PDEs from boundary sensing

We design a filter-based adaptive controller for stabilization of a system of n + 1 coupled linear hyperbolic partial differential equations (PDEs) with uncertain parameters from sensing limited to the boundary anti-collocated with the actuation. The only required knowledge about the system is the transport delay from the actuation to the sensing, and an upper bound on the transport delay in the reverse direction, as well as the parameter in the boundary condition collocated with the actuation. An interesting feature of the proposed design, is that the controller order does not increase with the number of states n. The theory is demonstrated in a simulation.