Initialization of the Shooting Method via the Hamilton-Jacobi-Bellman Approach
Initialization of the Shooting Method via the Hamilton-Jacobi-Bellman Approach
复制标题
通过 Hamilton-Jacobi-Bellman 方法初始化射击方法
DOI：
10.1007/s10957-010-9649-6
复制
发表时间：
2009
影响因子：
1.9
通讯作者：
P. Martinon
中科院分区：
文献类型：
--
作者：
E. Cristiani;P. Martinon
本文的目的是从数值的角度研究Hamilton-Jacobi-Bellman(HJB)方程与庞特里亚金最小原理(PMP)的耦合，以解决一些控制问题。使用HJB方法计算的值函数的粗略近似来获得PMP方法的初始猜测。与其他初始化技术(如连续或直接方法)相比，我们方法的优势在于提供了接近全局最小值的初始猜测。数值试验涉及多个极小值、不连续控制、奇异圆弧和状态约束。
The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniques (such as continuation or direct methods) is to provide an initial guess close to the global minimum. Numerical tests involving multiple minima, discontinuous control, singular arcs and state constraints are considered.