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

Shang, Peipei; Wang, Zhiqiang

doi:10.1016/j.jde.2010.09.003

Cited by 44 publications

(29 citation statements)

References 33 publications

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“…Sketch of proof. The proof for the simpler case b ≡ 0 and d ≡ 1 can be found in [32]. The more general case will be omitted here because of lack of space.…”

Section: B Non-local Pde Modelmentioning

confidence: 99%

Information Patterns in the Modeling and Design of Mobility Management Services

et al. 2018

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The development of sustainable transportation infrastructure for people and goods, using new technology and business models can prove beneficial or detrimental for mobility, depending on its design and use. The focus of this article is on the increasing impact new mobility services have on traffic patterns and transportation efficiency in general. Over the last decade, the rise of the mobile internet and the usage of mobile devices has enabled ubiquitous traffic information. With the increased adoption of specific smartphone applications, the number of users of routing applications has become large enough to disrupt traffic flow patterns in a significant manner. Similarly, but at a slightly slower pace, novel services for freight transportation and city logistics improve the efficiency of goods transportation and change the use of road infrastructure.The present article provides a general four-layer framework for modeling these new trends. The main motivation behind the development is to provide a unifying formal system description that can at the same time encompass system physics (flow and motion of vehicles) as well as coordination strategies under various information and cooperation structures. To showcase the framework, we apply it to the specific challenge of modeling and analyzing the integration of routing applications in today's transportation systems. In this framework, at the lowest layer (flow dynamics) we distinguish app users from non-app users. A distributed parameter model based on a non-local partial differential equation is introduced and analyzed.The second layer incorporates connected services (e.g., routing) and other applications used to optimize the local performance of the system. As inputs to those applications, we propose a third layer introducing the incentive design and global objectives, which are typically varying over the day depending on road and weather conditions, external events etc. The high-level planning is handled on the fourth layer taking social long-term objectives into account.We illustrate the framework by considering its ability to model at two different levels. Specific to vehicular traffic, numerical examples enable us to demonstrate the links between the traffic network layer and the routing decision layer. With a second example on optimized freight transport, we then discuss the links between the cooperative control layer and the lower layers. The congestion pricing in Stockholm is used to illustrate how also the social planning layer can be incorporated in future mobility services.A. Keimer and A. Bayen are with the Institute of Transportation Studies,

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“…Sketch of proof. The proof for the simpler case b ≡ 0 and d ≡ 1 can be found in [32]. The more general case will be omitted here because of lack of space.…”

Section: B Non-local Pde Modelmentioning

confidence: 99%

Information Patterns in the Modeling and Design of Mobility Management Services

et al. 2018

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“…We have the hidden regularity that f p 2 C 0 .OE0, 1; H 2 .0, T// in Theorem 3.2 (see [26,27] for the idea of proof ).…”

Section: Remark 32mentioning

confidence: 99%

Well‐posedness and exact controllability of the mass balance equations for an extrusion process

Shang

Wang

2015

Math Methods in App Sciences

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Communicated by T. LiIn this paper, we study the well-posedness and exact controllability of a physical model for an extrusion process in the isothermal case. The model expresses the mass balance in the extruder chamber and consists of a hyperbolic partial differential equation (PDE) and a nonlinear ordinary differential equation (ODE) whose dynamics describes the evolution of a moving interface. By suitable change of coordinates and fixed point arguments, we prove the existence, uniqueness, and regularity of the solution and finally, the exact controllability of the coupled system.

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“…The theoretical study of (2.1) is then more involved. A similar problem for h(t, y) =h(M 0 (t), y) is studied in [31].…”

Section: H(t Y)ϕ(t Y)dy (26)mentioning

confidence: 99%

Dimensional Reduction of a Multiscale Model Based on Long Time Asymptotics

Clément¹,

Coquel²,

Postel³

et al. 2017

Multiscale Model. Simul.

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Abstract. We consider a class of kinetic models for which a moment equation has a natural interpretation. We show that, depending on their velocity field, some models lead to moment equations that enable one to compute monokinetic solutions economically. We detail the example of a multiscale structured cell population model, consisting of a system of 2D transport equations. The reduced model, a system of 1D transport equations, is obtained by computing the moments of the 2D model with respect to one variable. The 1D solution is defined from the solution of the 2D model starting from an initial condition that is a Dirac mass in the direction removed by reduction. For arbitrary initial conditions, we compare 1D and 2D model solutions in asymptotically large time. Finite volume numerical approximations of the 1D reduced model can be used to compute the moments of the 2D solution with proper accuracy. The numerical robustness is studied in the scalar case, and a full scale vector case is presented.

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

Cited by 44 publications

References 33 publications

Information Patterns in the Modeling and Design of Mobility Management Services

Information Patterns in the Modeling and Design of Mobility Management Services

Well‐posedness and exact controllability of the mass balance equations for an extrusion process

Dimensional Reduction of a Multiscale Model Based on Long Time Asymptotics

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