This paper is concerned with a finite‐time nonlinear stochastic optimal control problem with input saturation as a hard constraint on the control input. The stochastic Hamilton‐Jacobi‐Bellman (SHJB) equation associated with this problem is derived, and a concrete solution method is also presented by extending an iteration framework of path integral stochastic optimal control. This is the first result that provides an optimal feedback control rigorously satisfying the saturation constraint as a solution to the SHJB equation. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

中文翻译：

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基于路径积分的具有输入饱和约束的非线性随机最优控制

本文关注的是具有输入饱和作为控制输入硬约束的有限时间非线性随机最优控制问题。推导了与此问题相关的随机Hamilton-Jacobi-Bellman（SHJB）方程，并通过扩展路径积分随机最优控制的迭代框架，提出了一种具体的求解方法。这是第一个提供严格满足饱和约束的最佳反馈控制作为SHJB方程的解决方案的结果。©2020日本电气工程师学会。由Wiley Periodicals LLC发布。