TY - JOUR
T1 - Stability analysis and numerical simulations of a one dimensional open channel hydraulic system
AU - Chentouf, Boumediène
AU - Smaoui, Nejib
N1 - Funding Information:
The authors acknowledge the support of Kuwait University.
Publisher Copyright:
© 2017 Elsevier Inc.
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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U2 - 10.1016/j.amc.2017.10.058
DO - 10.1016/j.amc.2017.10.058
M3 - Article
AN - SCOPUS:85034595134
SN - 0096-3003
VL - 321
SP - 498
EP - 511
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -