An Example of Solving HJB Equations Using Sparse Grid for Feedback Control
Paper (477.2Kb)Abstract
It is well known that solving the Hamilton-Jacobi-
Bellman (HJB) equation in moderate and high dimensions
(d > 3) suffers the curse of dimensionality. In this paper,
we introduce and demonstrate an example of solving the 6-D
HJB equation for the optimal attitude control of a rigid body
equipped with two pairs of momentum wheels. The system
is uncontrollable. To mitigate the curse-of-dimensionality, a
computational method based on sparse grids is introduced.
The method is causality free, which enjoys the advantage
of perfect parallelism. The problem is solved using several
hundred CPU cores in parallel. In the simulations, the solution
of the HJB equation is integrated into a model predictive control
for optimal attitude stabilization.
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