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

Abstract : 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∞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 LpLp-sense with 1⩽p⩽∞1⩽p⩽∞, the difference between the actual out-flux and a forecast demand over a fixed time period.
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https://hal.inria.fr/hal-00841189
Contributor : Frederique Clement <>
Submitted on : Thursday, July 4, 2013 - 10:10:30 AM
Last modification on : Thursday, December 10, 2020 - 12:34:03 PM

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Peipei Shang, Zhiqiang Wang. Analysis and control of a scalar conservation law modeling a highly re-entrant manufacturing system. Journal of Differential Equations, Elsevier, 2011, 250 (2), pp.949 - 982. ⟨10.1016/j.jde.2010.09.003⟩. ⟨hal-00841189⟩

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