Conference proceedings article
Function Approximation for the Deterministic Hamilton-Jacobi-Bellman Equation



Publication Details
Authors:
Rungger, M.; Stursberg, O.
Editor:
IEEE
Publisher:
IEEE
Place:
Shanghai, China
Publication year:
2009
Pages range:
2268-2273
Book title:
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on
ISBN:
978-1-4244-3871-6

Abstract
Based on Gaussian basis functions, a new method for calculating the Hamilton-Jacobi-Bellman equation for deterministic continuous-time and continuous-valued optimal control problems is proposed. A semi-Lagrangian discretization scheme is used to obtain a discrete-time finite-state approximation of the continuous dynamics. The value function of the discretized system is approximated by a Gaussian network. Limit behavior analysis provides a proof of convergence for the scheme. The performance of the presented approach is demonstrated for an underpowered inverted pendulum as numerical example. Furthermore, a comparison to the approximation by continuous piecewise affine functions (the current state of the art) shows the benefits of the approximation technique proposed here.


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Last updated on 2018-19-12 at 11:30