Controllability for a highly re-entrant manufacturing system with local and nonlocal velocity

In this paper, we study a scalar conservation law that models a high-volume, multistage continuous production through a re-entrant manufacturing system. The velocity has both local and nonlocal properties. We first prove the existence and uniqueness of the weak solution to the Cauchy problem with initial and boundary data in L∞ space. Based on this, a local exact controllability result is established, i.e., there exists a control that drives the weak solution from any given initial data to any desired final data around the origin in a certain time period.