A Causality Free Computational Method for HJB Equations with Application to Rigid Body Satellites
A Causality Free Computational Method for HJB Equations with Application to Rigid Body Satellites
复制标题
应用于刚体卫星的HJB方程无因果计算方法
DOI：
10.2514/6.2015-2009
复制
发表时间：
2015
影响因子：
9.7
通讯作者：
L. Wilcox
中科院分区：
文献类型：
--
作者：
Wei Kang;L. Wilcox
求解Hamilton-Jacobi-Bellman（HJB）方程是反馈最优控制的基本问题。利用HJB方程的解，反馈最优控制律可以以最小的计算量实时实现。然而，除了两个或三个状态变量的系统，数值求解HJB方程的一般非线性系统是不可行的，由于维数灾难。本文发展了一种求解HJB方程的新的计算方法。该方法是因果关系的自由，它享有的优势，在稀疏网格上的完美并行。与密集网格相比，稀疏网格具有显著减小的尺寸，这对于相对高维的系统是可行的，例如用于刚体姿态控制的6-D HJB方程。将该方法应用于动量轮卫星系统的最优姿态控制。在一组随机选择的样本点的数值解的准确性进行了验证。
Solving Hamilton-Jacobi-Bellman (HJB) equations is essential in feedback optimal control. Using the solution of HJB equations, feedback optimal control laws can be implemented in real-time with minimum computational load. However, except for systems with two or three state variables, numerically solving HJB equations for general nonlinear systems 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 enjoys the advantage of perfect parallelism on a sparse grid. Compared with dense grids, a sparse grid has a significantly 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 verified at a set of randomly selected sample points.