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

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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 CKWang, 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 p∈ [1,∞), the difference between the actual out-flux and a forecast demand over a fixed time period.