Controllability and stabilization of a conservation law modeling a highly re-entrant manufacturing system

In this paper, we study the controllability and stabilization for a scalar conservation law modeling a highly re-entrant manufacturing system with local and nonlocal velocity. We prove a local state controllability result, i.e., there exists a control that drives the solution from any given initial condition to any desired final condition in a certain time period, provided that the initial and final data are both close to the origin. A local result on nodal profile controllability is also given, i.e., for any initial data and any given out-flux in a neighborhood of the origin, there exists a control under which the solution starts from any initial data reaches exactly any desired out-flux over a fixed time period. Besides, using a Lyapunov function approach, we can stabilize the system to the origin exponentially by output feedback control.