De Saint-Venant equations-based model assessment in model predictive control of open channel flow

Model predictive control (MPC) is a model-based control technique that uses an optimization algorithm to generate optimal control actions. Based on the model used in optimization, MPC approaches can be categorized as linear or nonlinear. Both classes have advantages and disadvantages in terms of control accuracy and computational time. A typical linear model in open channel water management is the Integrator Delay (ID) model, while a nonlinear model usually refers to the Saint-Venant equations. In earlier work, we proposed the use of linearized Saint-Venant equations for MPC, where the model is formulated in a linear time-varying format and time-varying parameters are estimated outside of the optimization. Quadratic Programming (QP) is used to solve the optimization problem. However, the control accuracy of such an MPC scheme is not clear. In this paper, we compare this approach with an MPC scheme that uses Sequential Quadratic Programming (SQP) to solve the optimization problem. Because the estimation of the time-varying parameters is integrated in the optimization in SQP, the solutions from SQP-based MPC are expected to be superior to the solutions of QP-based approach. However, SQP can be computationally expensive. A simulation experiment illustrates that the QP-based MPC approach using a linearized Saint-Venant model has an accurate approximation of the control performance of SQP.