Nonlinear optimal control of cascaded irrigation canals with conservation law PDEs

Abstract

This paper considers an optimal control problem for cascaded irrigation canals. The aim of the optimal control is to guarantee both the minimum water levels for irrigation demands and avoidance of water overflows even dam collapse. Due to the structural complexities involving control gates and interconnected long-distance water delivery reaches that are modeled by the Saint-Venant PDEs with conservation laws, wave superposition effects, coupling effects and strong nonlinearities made the optimal control be a hard task. A nonlinear optimal control method is proposed to deal with the PDE-constrained optimization problem via a control parameterization approach. Control parameterization approximates the time-varying control by a linear combination of basis functions with control parameters. The Hamiltonian function method is used to derive the gradients of the objective function with respect to the control parameters as well as the time scale parameters for providing the search directions of the optimization problem with acceptable amount of computations. Based on the gradient formulas, a gradient-based optimization algorithm is proposed to solve the optimal control problem. The proposed nonlinear optimal control method is validated in two cases: a single reach canal in Yehe Irrigation District in Hebei Province (China) and a cascaded two-reach canal system.