Coordinating multiple Model Predictive Controllers for water reservoir networks operation

Abstract

Many large-scale water systems are formed by the interconnection of several sub-systems, whose different spatial and temporal characteristics make them strongly heterogeneous. The optimal management of such systems generally deals not only with issues related to large dimensionalities and strong nonlinearities, but also with the presence of several interactions between the sub-systems, which have a significant influence on the local control decisions and the overall system optimality. Real-Time Control, in the form of Model Predictive Control (MPC), has been gaining increasing prominence in the control of such systems, because of its ability in exploiting real-time information and forecasts. However, the practical implementation of MPC in a single monolithic centralized controller can be plagued by computational and reliability issues, especially when dealing with large-scale systems. On the other hand, the implementation of a decentralized control strategy, which neglects the interactions between the subsystems, can easily lead to sub-optimal performance. This calls for the design of coordination algorithms to provide a performance almost equivalent to that of a centralized control scheme while maintaining the existing decentralized structure. Early coordinated MPC formulations are based on the assumption that the exchange of predicted trajectory information between sub-systems is sufficient to account for the interactions. However this may not guarantee global optimality. Indeed, there needs to be cooperation between the controllers in addition to the communication of information and such observations form the crux of coordination strategies. The main tasks of the coordinator are to provide information to controllers, thus enabling them to derive interaction factors, and also to modify the local optimization problem such that the accumulated result of the local optimization problem is same as the result of the global one. The two common strategies used in the design of the coordinator are the interaction prediction and interaction balance principles. The former is based on predicting the correct inputs after taking into account the interaction effects: the local input variables are modified based on the effects of interactions between subsystems, which are calculated by the coordinator. The latter is based on predicting the correct interaction variables, where the coordination signals are based on the error between predicted and actual interaction variables. The purpose of this work is to show the applicability and utility of a coordinated control algorithm for the operation of water reservoir networks. The proposed algorithm aims at improving the existing decentralized controller performance without a significant increase in the computational effort. The algorithm capabilities are evaluated through numerical experiments on a water system composed of two multi-purpose reservoirs in cascade, for which the solution is provided with centralized, decentralized and coordinated control strategies. Preliminary results show the potential of the approach, which can provide a viable alternative to traditional decentralized methods in real-world applications.