An Adaptive Domain Decomposition Method for the Hamilton-Jacobi-Bellman Equation

机译：Hamilton-Jacobi-Bellman方程的自适应域分解方法

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摘要

In this paper, we propose an efficient algorithm for Hamilton-Jacobi-Bellman (HJB) equations governing a class of optimal feedback control problems. This algorithm is based on a non-overlapping domain decomposition method and an adaptive least-squares collocation radial basis function discretization with a novel matrix inversion technique. To demonstrate the accuracy and the effectiveness of this method, numerical experiments on test problems with up to three states and two control variables have been performed. The numerical results show that the proposed algorithm is a scalable parallel one and the computational costs decrease exponentially as the number of subdomains increases.

机译：在本文中，我们为控制一类最佳反馈控制问题的汉密尔顿-雅各比-贝尔曼（HJB）方程提出了一种有效的算法。该算法基于非重叠域分解方法和采用新型矩阵求逆技术的自适应最小二乘配置径向基函数离散化。为了证明这种方法的准确性和有效性，已经对多达三个状态和两个控制变量的测试问题进行了数值实验。数值结果表明，该算法是一种可扩展的并行算法，随着子域数量的增加，计算量呈指数下降。

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来源
《The 8th international conference on optimization: Techniques and Applications》|2010年|164-165|共2页
会议地点 Shanghai(CN)
作者
H.Alwardi; S.Wang; L.S.Jennings;
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作者单位

Department of Mathematics, Nizwa College of Applied Sciences,P O Box 699, PC 611 Nizwa, Sultanate of Oman;

School of Mathematics Statistics, The University of Western Australia,35 Stirling Hwy, Crawley 6009, Australia;

School of Mathematics Statistics, The University of Western Australia,35 Stirling Hwy, Crawley 6009, Australia;

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原文格式 PDF
正文语种 eng
中图分类系统优化;
关键词
HJB equation; optimal feedback control; least-squares collocation method; radial basis functions; shape parameter; adaptive method; domain decomposition; parallel computations;

机译：HJB方程;最优反馈控制;最小二乘配置法;径向基函数;形状参数;自适应法;域分解;并行计算;

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专利

1. An adaptive domain decomposition method for the Hamilton-Jacobi-Bellman equation [J] . H. Alwardi, S. Wang, L. S. Jennings Journal of Global Optimization . 2013,第4期

机译：Hamilton-Jacobi-Bellman方程的自适应域分解方法
2. Modified domain decomposition method for Hamilton-Jacobi-Bellman equations [J] . Guang-hua CHEN, Guang-ming CHEN, Zhi-hua DAI 应用数学和力学（英文版） . 2010,第012期

机译：Hamilton-Jacobi-Bellman方程的修正域分解方法
3. Modified domain decomposition method for Hamilton-Jacobi-Bellman equations [J] . 陈光华, 陈光明, 戴智华应用数学和力学：英文版 . 2010,第012期

机译：Hamilton-Jacobi-Bellman方程的修正域分解方法
4. An Adaptive Domain Decomposition Method for the Hamilton-Jacobi-Bellman Equation [C] . H.Alwardi, S.Wang, L.S.Jennings International conference on optimization: Techniques and Applications . 2010

机译：Hamilton-Jacobi-Bellman方程的自适应域分解方法
5. Parallel domain decomposition methods for stochastic partial differential equations and analysis of nonlinear integral equations. [D] . Jin, Chao. 2007

机译：随机偏微分方程的并行域分解方法和非线性积分方程的分析。
6. Non-conformal domain decomposition methods for time-harmonic Maxwell equations [O] . Yang Shao, Zhen Peng, Kheng Hwee Lim, -1

机译：时谐麦克斯韦方程组的非保形域分解方法
7. Domain-Dependence of Convergence Rate in Some Domain Decomposition Method for a Resolvent Stokes Equation (Computation mechanics and domain decomposition methods) [O] . 斉藤宣一 2000

机译：求解斯托克斯方程的某些域分解方法中收敛速度的域相关性（计算力学和域分解方法）

An Adaptive Domain Decomposition Method for the Hamilton-Jacobi-Bellman Equation

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