Abstract:

Based on the Saint-Venant equations, the star-shaped open channel network with bottom slope and bottom friction is studied in this paper. The system consists of $n$ subsystems: $n-1$ inlet channels and one outlet channel. It is assumed that both online output measurement and input control are located on the boundary. The feedback control law with a linear combination of position and delayed position is established based on the restriction of flow relation before and after the gate. Considering that the delay term can be characterized by the first-order hyperbolic partial differential equation, the closed-loop system is rewritten into the form of PDE-PDE infinite-dimensional coupling system by means of Riemannian coordinate transformation and linearization. By constructing the weighted Lyapunov function, the exponential stability of the system under the $L^2$-norm is discussed, and the sufficient conditions for the control parameters and time-delay value are given. Furthermore, it is proved that the online output measurement is regulated to the specified reference signal. Finally, numerical simulation is carried out by using Matlab to prove the rationality of the parameters conditions and the validity of the conclusion.

Key words: Saint-Venant equations, PDP feedback controller, Lyapunov method, Exponential stability