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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 \cite{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 .
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 -sense with
, the difference between the actual out-flux and a forecast
demand over a fixed time period.Comment: 32 pages, 12 figure
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