Hyperbolic Systems of Balance Laws

Bastin, Georges; Coron, Jean‐Michel

doi:10.1007/978-3-319-32062-5_1

Cited by 16 publications

(1 citation statement)

References 61 publications

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“…In recent years, the topic of controlling hyperbolic systems with PI controller has received a lot of attention (see, e.g. O’Dwyer, 4 Bastin et al, 5 and Bastin and Coron 6 ). For a scalar conservation law with PI boundary control in, 7 the stability conditions of feedback parameters were derived based on the Walton-Marshall stability criterion (see Walton and Marshall 8 ).…”

Section: Introductionmentioning

confidence: 99%

The PDP feedback control design and exponential stability for a star-shaped network of open channels

Zhao

Pang

Guo

et al. 2023

Advances in Mechanical Engineering

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This paper investigates the stability of a star-shaped network of open channels under the position and delayed position (PDP) feedback controller. Firstly, we deal with the special case of a single channel, and the well-posedness and exponential stability of the closed-loop system are established by using the semi-group theory and a strict Lyapunov function. The explicit dissipative conditions for system parameters and time-delay are presented. Then, we analyze the delay-independent stability of the closed-loop system by the method of characteristic. Next, we extend the PDP control design to the star-shaped network of [Formula: see text] channels with [Formula: see text] inlet channels and one outlet channel, and the exponential stability can be obtained similarly. Finally, we give some numerical simulations for the special case of three channels.

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Section: Introductionmentioning

confidence: 99%

The PDP feedback control design and exponential stability for a star-shaped network of open channels

Zhao

Pang

Guo

et al. 2023

Advances in Mechanical Engineering

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Boundary Control of 1-D Hyperbolic Systems

Bastin

Coron

2021

Encyclopedia of Systems and Control

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Contributions to the Problem of High-Gain Observer Design for Hyperbolic Systems

Kitsos

Besan

Prieur

2021

Lecture Notes in Control and Information Sciences

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This chapter proposes some non-trivial extensions of the classical highgain observer designs for finite-dimensional nonlinear systems to some classes of infinite-dimensional systems, written as triangular systems of coupled first-order hyperbolic partial differential equations (PDEs), where an observation of one coordinate of the state only is considered as the system's output. These forms may include some epidemic models and tubular chemical reactors. To deal with this problem, depending on the number of distinct velocities of the hyperbolic system, direct and indirect observer designs are proposed. We first show intuitively how direct observer design can be applied to quasilinear partial integro-differential hyperbolic systems of balance laws with a single velocity, as a natural extension of the finitedimensional case. We then introduce an indirect approach for systems with distinct velocities (up to three velocities), where an infinite-dimensional state transformation first maps the system into a suitable systems of Partial Differential Equations (PDEs) and the convergence of the observer is subsequently exhibited in appropriate norms. This indirect approach leads to the use of spatial derivatives of the output in the observer dynamics.

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Hyperbolic Systems of Balance Laws

Cited by 16 publications

References 61 publications

The PDP feedback control design and exponential stability for a star-shaped network of open channels

The PDP feedback control design and exponential stability for a star-shaped network of open channels

Boundary Control of 1-D Hyperbolic Systems

Contributions to the Problem of High-Gain Observer Design for Hyperbolic Systems

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