A Causality Free Computational Method for HJB Equations with Application to Rigid Body Satellites
Paper (432.7Kb)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.
Description
The article of record as published may be found at http://dx.doi.org/10.2414/62015-2009
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.Collections
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