Stability analysis and numerical simulations of a one dimensional open channel hydraulic system

Boumediène Chentouf; Nejib Smaoui

doi:10.1016/j.amc.2017.10.058

Stability analysis and numerical simulations of a one dimensional open channel hydraulic system

Boumediène Chentouf^*, Nejib Smaoui

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

This paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river. First, an output feedback control is proposed. Next, the closed-loop system is proved to possess a unique solution in a functional space. Furthermore, the spectrum and resolvent sets of the system operator are characterized. Then, stability results are stated and proved according to a smallness assumption on the feedback gain. The proof invokes Lyapunov direct method. Last but not least, we adopt the Chebychev collocation method, that uses backward Euler method and the Gauss-Lobatto points, to provide numerical simulations in order to ascertain the correctness of the theoretical outcomes.

Original language	English
Pages (from-to)	498-511
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	321
DOIs	https://doi.org/10.1016/j.amc.2017.10.058
Publication status	Published - Mar 15 2018
Externally published	Yes

Keywords

Chebychev collocation method
Open channel hydraulic system
Output boundary feedback control
Stability

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2017.10.058

Cite this

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title = "Stability analysis and numerical simulations of a one dimensional open channel hydraulic system",

abstract = "This paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river. First, an output feedback control is proposed. Next, the closed-loop system is proved to possess a unique solution in a functional space. Furthermore, the spectrum and resolvent sets of the system operator are characterized. Then, stability results are stated and proved according to a smallness assumption on the feedback gain. The proof invokes Lyapunov direct method. Last but not least, we adopt the Chebychev collocation method, that uses backward Euler method and the Gauss-Lobatto points, to provide numerical simulations in order to ascertain the correctness of the theoretical outcomes.",

keywords = "Chebychev collocation method, Open channel hydraulic system, Output boundary feedback control, Stability",

author = "Boumedi{\`e}ne Chentouf and Nejib Smaoui",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2018",

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T1 - Stability analysis and numerical simulations of a one dimensional open channel hydraulic system

AU - Chentouf, Boumediène

AU - Smaoui, Nejib

PY - 2018/3/15

Y1 - 2018/3/15

N2 - This paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river. First, an output feedback control is proposed. Next, the closed-loop system is proved to possess a unique solution in a functional space. Furthermore, the spectrum and resolvent sets of the system operator are characterized. Then, stability results are stated and proved according to a smallness assumption on the feedback gain. The proof invokes Lyapunov direct method. Last but not least, we adopt the Chebychev collocation method, that uses backward Euler method and the Gauss-Lobatto points, to provide numerical simulations in order to ascertain the correctness of the theoretical outcomes.

AB - This paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river. First, an output feedback control is proposed. Next, the closed-loop system is proved to possess a unique solution in a functional space. Furthermore, the spectrum and resolvent sets of the system operator are characterized. Then, stability results are stated and proved according to a smallness assumption on the feedback gain. The proof invokes Lyapunov direct method. Last but not least, we adopt the Chebychev collocation method, that uses backward Euler method and the Gauss-Lobatto points, to provide numerical simulations in order to ascertain the correctness of the theoretical outcomes.

KW - Chebychev collocation method

KW - Open channel hydraulic system

KW - Output boundary feedback control

KW - Stability

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EP - 511

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Stability analysis and numerical simulations of a one dimensional open channel hydraulic system

Abstract

Keywords

ASJC Scopus subject areas

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