PIECEWISE AFFINE APPROXIMATIONS FOR THE CONTROL OF A ONE-RESERVOIR HYDROELECTRIC SYSTEM

We analyze the computation of optimal and approximately optimal polici es for a discrete-time model of a single reservoir whose discharges ge nerate hydroelectric power. Inflows in successive periods are random v ariables. Revenue from hydroelectric production is represented by a pi ecewise linear function. We use the special structure of optimal polic ies, together with piecewise affine approximations of the optimal retu rn functions at each stage of dynamic programming, to decrease the com putational effort by an order of magnitude compared with ordinary valu e iteration. The method is then used to obtain easily computable lower and upper bounds on the value function of an optimal policy, and a po licy whose value function is between the bounds.