Gas Flow in Fan-Shaped Networks: Classical Solutions and Feedback Stabilization

Gugat, Martin; Dick, Markus; Leugering, Günter

doi:10.1137/100799824

Cited by 72 publications

(74 citation statements)

References 22 publications

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“…Remark 1: The system (2) is a generalization of the Euler equations for a nonstationary state in a local C 1 -neighborhood of a stationary subcritical state (see [6], [9], [10], [11], [12]). In particular, for the Euler equations we have…”

Section: B Quasilinear Systemmentioning

confidence: 99%

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Feedback stabilization of quasilinear hyperbolic systems with varying delays

Dick

Gugat

Leugering

2012

2012 17th International Conference on Methods &Amp; Models in Automation &Amp; Robotics (MMAR)

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We consider the feedback stabilization of quasilinear hyperbolic systems on star-shaped networks. We present boundary feedback controls with varying delays. The delays are given by C 1 -functions with bounded derivatives. We obtain the existence of unique C 1 -solutions on a given finite time interval. In order to measure the system evolution, we introduce an L 2 -Lyapunov function with delay terms. The feedback controls yield the exponential decay of the Lyapunov function with time. This implies the exponential stability of the system. Our results can be applied on the stabilization of the isothermal Euler equations with friction that model the gas flow in pipe networks.

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Section: B Quasilinear Systemmentioning

confidence: 99%

“…A method to stabilize a star-shaped network of vibrating strings governed by the wave equation is presented in [14]. In [6], [10], [12] the stabilization of the Euler equations on networks of pipes and compressors without time delay is considered.…”

Section: Introductionmentioning

confidence: 99%

Feedback stabilization of quasilinear hyperbolic systems with varying delays

Dick

Gugat

Leugering

2012

2012 17th International Conference on Methods &Amp; Models in Automation &Amp; Robotics (MMAR)

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“…It is worth pointing out that hyperbolic equations have important applications in the modeling and control of physical networks. Besides road traffic networks (Coclite et al (2005)), as previously discussed, one can highlight other examples such as hydraulic networks Bastin et al (2008) and gas pipeline networks Gugat et al (2011). This paper deals with stability analysis of a communication network which is modeled using the fluid-flow and compartmental setting, combining hyperbolic conservation laws with ordinary differential equations.…”

Section: Introductionmentioning

confidence: 97%

Fluid-flow modeling and stability analysis of communication networks

et al. 2017

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This paper deals with a fluid-flow modeling under compartmental representation of a network. The motivating example is a communication network made up of buffers and transmission lines where densities and flows of packets are viewed as macroscopic variables respecting the conservation laws. The main contribution lies in the resulting model. It is a coupled linear hyperbolic partial differential equations (PDEs) with an ordinary differential equation (ODEs) along with a dynamic boundary condition. Input-to-state stability of an optimal equilibrium is analyzed using Lyapunov techniques.

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“…Among the different networks, we have in mind the hydraulic networks (see [3], [4]), road traffic networks (see [12]), or gas pipeline networks (see [7]). Due to the range of those applications in the engineering field, an important research on the theorical aspects in modelling and control of such systems is made.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov techniques for stabilization of switched linear systems of conservation laws

Lamare

Girard

Prieur

2013

52nd IEEE Conference on Decision and Control

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Abstract-In this paper, the exponential stability in L 2 -norm is investigated for a class of switched linear systems of conservation laws. The state equations and the boundary conditions are both subject to switching. We consider the problem of synthesizing stabilizing switching controllers. By means of Lyapunov techniques, three control strategies are developed based on steepest descent selection, possibly combined with a hysteresis and a low-pass filter. Some numerical examples are considered to illustrate our approach and to show the merits of the proposed strategies.

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Gas Flow in Fan-Shaped Networks: Classical Solutions and Feedback Stabilization

Cited by 72 publications

References 22 publications

Feedback stabilization of quasilinear hyperbolic systems with varying delays

Feedback stabilization of quasilinear hyperbolic systems with varying delays

Fluid-flow modeling and stability analysis of communication networks

Lyapunov techniques for stabilization of switched linear systems of conservation laws

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