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 |
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Pages (from-to) | 498-511 |
Number of pages | 14 |
Journal | Applied Mathematics and Computation |
Volume | 321 |
DOIs | |
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