Model Predictive Control Of Open-channel Systems Based On Koopman Operator

Saint-venant hydraulic dynamic model of open-channel systems is a set of nonlinear partial differential equations,which can’t be solved directly,so it’s difficult to be directly used in control strategy design.At present,most of the open-channel systems modeling are based on the discretization or linearization of Saint-Venant equations,and the simplified model decreases it’s accuracy over time,affecting the stability of the model.In this paper,the koopman model of open-channel systems are obtained by processing the actual data of open-channel systems.Based on the established model,the centralized model predictive control strategy and the distributed model predictive control strategy are designed.Firstly,SICC simulation software is used to generate simulation data set of open-channel systems,koopman operator and extended dynamic model decomposition method are used to process the data set,and the system matrix is solved,and the high-dimensional linear koopman model of open channel system is obtained.The validity and accuracy of the model are verified by simulation.Secondly,the koopman model is used as the prediction model,and the centralized model predictive controller is designed based on the model predictive control method.By outputting the optimal controller sequence solved by Matlab software to SICC software,the simulation experiment is completed,which verifies the effectiveness of the koopman model centralized predictive control algorithm for open-channel systems.Finally,koopman model distributed predictive control is designed for open-channel systems because it’s a complex distributed systems and the application of centralized model predictive control is limited.The openchannel systems are divided into multiple subsystems,and each subsystem designs a distributed controller separately.By solving Nash optimal solution,it’s the target value of system stability tracking.The comparison between koopman model distributed predictive control and centralized predictive control is completed through simulation,and the superiority of distributed predictive control calculation is verified.