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

Jean Michel Coron, Matthias Kawski, Zhiqiang Wang

Research output: Contribution to journalArticle

26 Scopus citations

Abstract

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 L1-data, and study their regularity properties. We also prove the existence of optimal controls that minimizes in the L2-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.

Original languageEnglish (US)
Pages (from-to)1337-1359
Number of pages23
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume14
Issue number4
DOIs
StatePublished - Nov 1 2010

Keywords

  • Conservation law
  • Optimal control
  • Re-entrant manufacturing system

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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