A first-order approximation to stochastic optimal control of reservoirs
type: Item
instance of: scholarly article
title: A first-order approximation to stochastic optimal control of reservoirs
zbMATH Open document ID: 0658.76094
DOI: 10.1007/BF01543889
published in: Stochastic Hydrology and Hydraulics
publication date: 1987-01-01T00:00:00Z
review text: A new approximate method of solution for stochastic optimal control problems with many state and control variables is introduced. The method is based on the expansion of the optimal control into the deterministic feedback control plus a caution term. The analytic, small-perturbation calculation of the caution term is at the heart of the new method. The developed approximation depends only on the first two statistical moments of the random inputs and up to the third derivatives of the cost functions. Its computational requirements do not exhibit the exponential growth exhibited by discrete stochastic DP and can be used as a suboptimal solution to problems for which application of stochastic DP is not feasible. The method is accurate when the cost-to-go functions are approximately cubic in a neighbourhood around the deterministic trajectory whose size depends on forecasting uncertainty. Furthermore, the method elucidates the stochastic optimization problem yielding insights which cannot be easily obtained from the numerical application of discrete DP.
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4076882
zbMATH Keywords: approximate method of solution
zbMATH Keywords: stochastic optimal control poblems
zbMATH Keywords: deterministic feedback control
zbMATH Keywords: analytic, small-perturbation calculation
zbMATH Keywords: suboptimal solution
author: Peter K. Kitanidis
MaRDI profile type: Publication
cites work: Q3241581
cites work: Q5737099
cites work: Q3292915
cites work: Discretional Convexity and the Maximum Principle for Discrete Systems
cites work: Q5628775
cites work: Q5836597
cites work: Perturbation methods and non-linear hyperbolic waves
description: scientific article; zbMATH DE number 4076882