Diagnostic Checking in Stochastic Dynamic Programming

Abstract

A testing procedure to diagnose whether the stochastic dynamic programming (SDP) models for reservoir operations will converge is presented. Theoretically, the stability of SDP can be diagnosed by checking whether a coefficient matrix, connected with the existence and uniqueness of solutions of transition probabilities for the inflows, is linearly independent. The steady‐state SDP model of reservoir operations is guaranteed after the SDP convergence has been approved. If the rank of the coefficient matrix is the same as the number of inflow states, there is precisely one solution for the steady‐state distribution of inflows and SDP convergence will be reached. Otherwise, the SDP model is divergent.