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November  2010, 14(4): 1337-1359. doi: 10.3934/dcdsb.2010.14.1337

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

Jean-Michel Coron 1, , Matthias Kawski 2, and  Zhiqiang Wang 3,

1. 

Institut universitaire de France and Université Pierre et Marie Curie-Paris VI, UMR 7598, Laboratoire Jacques-Louis Lions, 4, place Jussieu, Paris, F-75005, France
2. 

Arizona State University, Tempe, Arizona 85287-1804, United States
3. 

Fudan University and Université Pierre et Marie Curie-Paris VI, UMR 7598, Laboratoire Jacques-Louis Lions, 4, place Jussieu, Paris, F-75005, France

Received  July 2009 Revised  March 2010 Published  August 2010

This article studies a hyperbolic conservation law that models a highly re-entrant manufacturing system as encountered in semi-conductor production. Characteristic features are the nonlocal character of the velocity and that the influx and outflux constitute the control and output signal, respectively. We prove the existence and uniqueness of solutions for $L^1$-data, and study their regularity properties. We also prove the existence of optimal controls that minimizes in the $L^2$-sense the mismatch between the actual and a desired output signal. Finally, the time-optimal control for a step between equilibrium states is identified and proven to be optimal.
Keywords: conservation law, re-entrant manufacturing system., Optimal control.
Mathematics Subject Classification: Primary: 35L65, 49J20, 93C2.
Citation: Jean-Michel Coron, Matthias Kawski, Zhiqiang Wang. Analysis of a conservation law modeling a highly re-entrant manufacturing system. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1337-1359. doi: 10.3934/dcdsb.2010.14.1337
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