Lyapunov-based boundary feedback control in multi-reach canals

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. 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)