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Lyapunov-based boundary feedback control in multi-reach canals

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Abstract

This paper presents a Lyapunov-based approach to design the boundary feedback control for an openchannel network composed of a cascade of multi-reach canals, each described by a pair of Saint-Venant equations. The weighted sum of entropies of the multi-reaches is adopted to construct the Lyapunov function. The time derivative of the Lyapunov function is expressed by the water depth variations at the gate boundaries, based on which a class of boundary feedback controllers is presented to guarantee the local asymptotic closed-loop stability. The advantage of this approach is that only the water level depths at the gate boundaries are measured as the feedback.

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Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China

    LiHui Cen & YuGeng Xi

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  1. LiHui Cen
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  2. YuGeng Xi
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Correspondence to YuGeng Xi.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 60504026, 60674041), and the National High-Tech Research & Development Program of China (Grant No. 2006AA04Z173)

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Cen, L., Xi, Y. Lyapunov-based boundary feedback control in multi-reach canals. Sci. China Ser. F-Inf. Sci. 52, 1157–1164 (2009). https://doi.org/10.1007/s11432-009-0108-7

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  • DOI: https://doi.org/10.1007/s11432-009-0108-7

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