A Causality Free Computational Method for HJB Equations with Application to Rigid Body Satellites
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Authors
Wilcox, Lucas
Kang, Wei
Subjects
Advisors
Date of Issue
2015-01
Date
January 2015
Publisher
Language
Abstract
Solving Hamilton-Jacobi-Bellman (HJB) equations is essential in feedback optimal con-
trol. Using the solution of HJB equations, feedback optimal control laws can be imple-
mented in real-time with minimum computational load. However, except for systems with
two or three state variables, numerically solving HJB equations for general nonlinear sys-
tems is unfeasible due to the curse of dimensionality. In this paper, we develop a new
computational method of solving HJB equations. The method is causality free, which en-
joys the advantage of perfect parallelism on a sparse grid. Compared with dense grids,
a sparse grid has a signi cantly reduced size which is feasible for systems with relatively
high dimensions, such as 6-D HJB equations for the attitude control of rigid bodies. The
method is applied to the optimal attitude control of a satellite system using momentum
wheels. The accuracy of the numerical solution is veri ed at a set of randomly selected
sample points.
Type
Conference Paper
Description
The article of record as published may be found at http://dx.doi.org/10.2414/62015-2009
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
AFOSR
NRL
NRL
Funder
Format
10 p.
Citation
AIAA SciTech
5-9 January 2015, Kissimmee, Florida
AIAA Guidance, Navigation, and Control Conference, AIAA 2015-2009
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.