A collocation-based approach to solve the finite horizon Hamilton-Jacobi-Bellman equation
A collocation-based approach to solve the finite horizon Hamilton-Jacobi-Bellman equation
复制标题
基于配置的有限视野 Hamilton-Jacobi-Bellman 方程求解方法
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
M. Majji
中科院分区：
文献类型：
--
作者：
Michael Mercurio;Nagavenkat Adurthi;P. Singla;M. Majji
本文提出了一种通过求解有限时间汉密尔顿Jacobi Ballman方程来获得最优反馈控制律的方法。求解HJB方程的传统方法受到维数灾难的影响，因为空间变量的数量等于状态维数，这是机械系统自由度数量的两倍。所提出的方法利用最近开发的非积求积方法称为共轭无迹变换（CUT）结合稀疏近似工具，设计一种配置方法来解决HJB方程的计算效率的方式。数值模拟结果，以评估所提出的想法的有效性。
This paper presents an approach to derive the optimal feedback control laws by solving the finite time Hamilton Jacobi Ballman equation. Conventional methods to solve the HJB equation suffer from curse of dimensionality as the number of spatial variables is equal to the state dimension, which is twice the number of degrees of freedom of a mechanical system. The presented approach exploits the recently developed non-product quadrature method known as Conjugate Unscented Transformation (CUT) in conjunction with sparse approximation tools to devise a collocation method to solve the HJB equation in a computationally efficient manner. Numerical simulation results are presented to assess the efficacy of the proposed ideas.