Nonlinear optimal control of an open-channel hydraulic system based on an infinite-dimensional model

A nonlinear optimal control approach based on an infinite-dimensional model is presented which determines the optimal opening of a regulator gate at the upstream end in the case of a single reach hydraulic system, in order to minimize the waste water and the variation of the water depth. The effectiveness of the control algorithm is demonstrated by a simulation example. The simulation results show good improvements in reducing the variation of water depth compared to the uncontrolled case. The Saint-Venant equations and their adjoint equations have been solved numerically by using a nonlinear implicit integration scheme (the Preissmann scheme). Our main contribution is the solution of an open-channel control problem which includes a distributed parameter model, with nonlinearities, friction, canal slope, an adjustable regulator gate and a pumping station, via variational calculus.