An Optimal Approximate Dynamic Programming Algorithm for Concave, Scalar Storage Problems With Vector-Valued Controls

We prove convergence of an approximate dynamic programming algorithm for a class of high-dimensional stochastic control problems linked by a scalar storage device, given a technical condition. Our problem is motivated by the problem of optimizing energy flows for a power grid supported by grid-level...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 58; no. 12; pp. 2995 - 3010
Main Authors: Nascimento, Juliana, Powell, Warren B.
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2013
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Approximate dynamic programming
Approximation algorithms
Convergence
Dynamic programming
Function approximation
Piecewise linear approximation
resource allocation
storage
Vectors
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:We prove convergence of an approximate dynamic programming algorithm for a class of high-dimensional stochastic control problems linked by a scalar storage device, given a technical condition. Our problem is motivated by the problem of optimizing energy flows for a power grid supported by grid-level storage. The problem is formulated as a stochastic, dynamic program, where we estimate the value of resources in storage using a piecewise linear value function approximation. Given the technical condition, we provide a rigorous convergence proof for an approximate dynamic programming algorithm, which can capture the presence of both the amount of energy held in storage as well as other exogenous variables. Our algorithm exploits the natural concavity of the problem to avoid any need for explicit exploration policies.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2013.2272973