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A RIESZ BASIS METHODOLOGY FOR PROPORTIONAL AND INTEGRAL OUTPUT REGULATION OF A ONE-DIMENSIONAL DIFFUSIVE-WAVE EQUATION.
- Source :
- SIAM Journal on Control & Optimization; 2008, Vol. 47 Issue 5, p2275-2302, 28p, 9 Graphs
- Publication Year :
- 2008
-
Abstract
- In this article, we consider a dam-river system modeled by a diffusive-wave equation. This model is commonly used in hydraulic engineering to describe dynamic behavior of the unsteady flow in a river for shallow water when the flow variations are not important. In order to stabilize and regulate the system, we propose a proportional and integral boundary controller. Contrary to many physical systems, we end up with a nondissipative closed-loop system with noncollocated actuators and sensors. We show that the closed-loop system is a Riesz spectral system and generates an analytic semigroup. Then, we shall be able to assign the spectrum of the closed-loop system in the open left half-plane to ensure its exponential stability as well as the output regulation independently of any known or unknown constant perturbation. These results are illustrated by several numerical examples. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03630129
- Volume :
- 47
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Control & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 35246580
- Full Text :
- https://doi.org/10.1137/060671188