Analysis and control of a scalar conservation law modeling a highly re-entrant manufacturing system

In this paper, we study a scalar conservation law that models a highly re-entrant manufacturing system as encountered in semi-conductor production. As a generalization of Coron et al. (2010) [14], the velocity function possesses both the local and nonlocal character. We prove the existence and uniqueness of the weak solution to the Cauchy problem with initial and boundary data in L∞. We also obtain the stability (continuous dependence) of both the solution and the out-flux with respect to the initial and boundary data. Finally, we prove the existence of an optimal control that minimizes, in the Lp-sense with 1⩽p⩽∞, the difference between the actual out-flux and a forecast demand over a fixed time period.