Stabilization of a One-Dimensional Dam-River System: Nondissipative and Noncollocated Case

B. Chentouf () and J. M. Wang
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B. Chentouf: Sultan Qaboos University
J. M. Wang: Beijing Institute of Technology

Journal of Optimization Theory and Applications, 2007, vol. 134, issue 2, No 5, 223-239

Abstract: Abstract In this paper, we consider a one-dimensional dam-river system, described by a diffusive-wave equation and often used in hydraulic engineering to model the dynamic behavior of the unsteady flow in a river for shallow water when the flow variations are not important. We propose an integral boundary control which leads to a nondissipative closed-loop system with noncollocated actuators and sensors; hence, two main difficulties arise: first, how to show the C 0-semigroup generation and second, how to achieve the stability of the system. To overcome this situation, the Riesz basis methodology is adopted to show that the closed-loop system generates an analytic semigroup. Concerning the stability, the shooting method is applied to assign the spectrum of the system in the open left-half plane and ensure its exponential stability as well as the output regulation. Numerical simulations are presented for a family of system parameters.

Keywords: Diffusive-wave equations; Analytic semigroups; Riesz spectral operators; Stability; Robust output regulation (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-007-9223-z

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