Analysis and control of a scalar conservation law modeling a highly re-entrant manufacturing system
By Peipei Shang, Zhiqiang Wang. 2010
52 citations recorded by the source corpus.
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 ∞ . 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 L p -sense with 1 ⩽ p ⩽ ∞ , the difference between the actual out-flux and a forecast demand over a fixed time period.
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e7a6790ac10a9d30969102e8d5ddfdd00d2c7ee9
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In Applied Mathematics
- Jean-Michel Coron
- Alexander Keimer
- Lukas Pflug
- G. Bastin
- Giuseppe Maria Coclite
- Rafael Vazquez
- Miroslav Krstic
- Zhaoyang Yin
In Control and Systems Engineering
- G. Bastin
- Jean-Michel Coron
- Alexander Keimer
- Lukas Pflug
- Giuseppe Maria Coclite
- Miroslav Krstic
- Rafael Vazquez
- Eduardo Cerpa
In Mathematical Physics
- Jean-Michel Coron
- G. Bastin
- Alexander Keimer
- Lukas Pflug
- Giuseppe Maria Coclite
- Eduardo Cerpa
- Olivier Glass
- Miroslav Krstic
Citations in the corpus
- A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels (2020, background): “Nonlocal conservation laws have been studied and analyzed quite intensively over the last decade from an application point of view with a particular focus on traffic flow [5, 20, 30, 45, 53, 37], supply chains [39, 55, 32], pedestrian flow/crowd dynamics [21], opinion formation [2, 51], chemical eng”
- Stability and Boundary Stabilization of 1-D Hyperbolic Systems (2016, methodology): “Another stability condition is stated in the following Theorem by Silkowski (1976) which relies on the Kronecker density theorem (e.”