19. Stochastic and Robust Control of Water Resource Systems: Concepts, Methods and Applications

In order for water resources management to effectively cope with all the key drivers of global change (climate, demographic, economic, social, policy/law/institutional, and technology changes), it is essential that the traditional sector-by-sector management approach to water resources is transformed into a new paradigm, where water is considered as the principal and cross cutting medium for balancing food, energy security, and environmental sustainability. One major technical challenge in expanding the scope of water resources management across sectors and to the river basin level is to develop new methodologies and tools to cope with the increasing complexity of water systems. When dealing with large water resources systems, particularly with water reservoir networks, traditional non-linear, stochastic control approaches, like Stochastic Dynamic Programming (SDP), suffer from the curse of dimensionality that makes them essentially unusable. In this chapter we review the most advanced, general approaches available to overcome, or at least effectively mitigate, SDP limits in dealing with large water reservoir networks. Depending on the strategy adopted to alleviate the dimensionality burden we distinguish two classes of approaches: methods based on the restriction of the degrees of freedom of the control problem and methods based on the simplification of the water system model. Emphasis is given to the technical implications of the high dimension and highly non-linear nature of water reservoir systems and to the human dimension component involved in their operation. For each approach a real world numerical application is briefly presented.