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