Controlled Approximation of the Stochastic Dynamic Programming Value Function for Multi-Reservoir Systems

We present an approximation of the Stochastic Dynamic Programming (SDP) value function based on a partition of the state space into simplices. The vertices of such simplices form an irregular grid over which the value function is computed. Under convexity assumptions, lower and upper bounds are developed over the state space continuum. The partition is then refined where the gap between these bounds is largest. This process readily provides a controllable trade-off between accuracy and solution time.