Water reservoirs management under uncertainty by approximating networks and learning from data

Finite-horizon management of water reservoirs systems under uncertainty can be formalized as a T-stage stochastic optimal-control problem. As is well known, T-stage stochastic optimal-control problems can be solved analytically by dynamic programming (DP), if suitable hypotheses on the state equation, the cost function, and the random variables (river inflows and stochastic rain inflows) are verified. A realistic model for water management tasks has to take into account the presence of uncertainties, represented, for example, by river inflows and stochastic rain inflows. This makes things more complex as in such a case, the random variables have to be discretized, too. When stochastic DP is used, the efforts to cope with the curse of dimensionality have followed two main approaches: simplification of the problem by using simpler models and use of smart approximators for the cost-to-go functions. © 2007 Elsevier Ltd. All rights reserved.