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

By Jean-Michel Coron, Matthias Kawski, Zhiqiang Wang. 2009

70 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7f1c90a4304dd834bc29217c46490c594efe6fa2

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow (2011, methodology): “This last model was studied for example in [10], imposing boundary conditions in x = 0 and x = 1.”
Analysis and control of a scalar conservation law modeling a highly re-entrant manufacturing system (2010, methodology): “This cost functional is motivated by [14,23] and the existence of the solution to this optimal control problem is obtained by the following theorem.”
A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels (2020, background): “Our “nonlocal-to-local convergence” result closes the gap between local and nonlocal modelling of phenomena governed by conservation laws; moreover, it provides a way of defining the entropy admissible solutions of local conservation laws as limits of weak solutions to nonlocal conservation laws, wh”