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Quadratic approximate dynamic programming for input‐affine systems
Author(s) -
Keshavarz Arezou,
Boyd Stephen
Publication year - 2014
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2894
Subject(s) - affine transformation , semidefinite programming , quadratically constrained quadratic program , mathematical optimization , quadratic programming , quadratic equation , convex optimization , simple (philosophy) , regular polygon , dynamic programming , computer science , mathematics , second order cone programming , stochastic programming , value (mathematics) , philosophy , geometry , epistemology , machine learning , pure mathematics
SUMMARY We consider the use of quadratic approximate value functions for stochastic control problems with input‐affine dynamics and convex stage cost and constraints. Evaluating the approximate dynamic programming policy in such cases requires the solution of an explicit convex optimization problem, such as a quadratic program, which can be carried out efficiently. We describe a simple and general method for approximate value iteration that also relies on our ability to solve convex optimization problems, in this case, typically a semidefinite program. Although we have no theoretical guarantee on the performance attained using our method, we observe that very good performance can be obtained in practice.Copyright © 2012 John Wiley & Sons, Ltd.