A non-linear backstepping like controller for a three-point collocation model of water flow dynamics

This paper is devoted to the non-linear control of irrigation canals or dam-river systems. Open-channel dynamics are based on the well-known Saint-Venant non-linear partial differential equations. Here, a finite-dimensional model previously developed, and based on a collocation Galerkin method together with a functional approximation by Lagrange polynomials, is used as a basic model for control. In a previous paper it has indeed been shown how such a model is much more tractable than those obtained from classical finite-difference or finite-element methods (from the viewpoint of both state dimension and structure) and well suited to control purposes. In this paper we show how this model can be used to design a non-linear controller using backstepping techniques for the goal of controlling water levels along an open-channel reach, and we present some simulation of the system with the obtained controller.