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Paper details
Number 2 - June 2020
Volume 30 - 2020
A linear programming methodology for approximate dynamic programming
Henry Díaz, Antonio Sala, Leopoldo Armesto
Abstract
The linear programming (LP) approach to solve the Bellman equation in dynamic programming is a well-known option for
finite state and input spaces to obtain an exact solution. However, with function approximation or continuous state spaces,
refinements are necessary. This paper presents a methodology to make approximate dynamic programming via LP work
in practical control applications with continuous state and input spaces. There are some guidelines on data and regressor
choices needed to obtain meaningful and well-conditioned value function estimates. The work discusses the introduction of
terminal ingredients and computation of lower and upper bounds of the value function. An experimental inverted-pendulum
application will be used to illustrate the proposal and carry out a suitable comparative analysis with alternative options in
the literature.
Keywords
linear programming, approximate dynamic programming, control applications, neural networks