In this paper we propose a new methodology for decision-making under uncertainty using recent advancements in the areas of nonlinear stochastic optimal control theory, applied mathematics, and machine learning. Grounded on the fundamental relation between certain nonlinear partial differential equations and forward-backward stochastic differential equations, we develop a control framework that is scalable and applicable to general classes of stochastic systems and decision-making problem formulations in robotics and autonomy. The proposed deep neural network architectures for stochastic control consist of recurrent and fully connected layers. The performance and scalability of the aforementioned algorithm are investigated in three non-linear systems in simulation with and without control constraints. We conclude with a discussion on future directions and their implications to robotics.
翻译:在本文中,我们建议采用非线性随机最佳控制理论、应用数学和机器学习领域的最新进展,在不确定情况下采用新的决策方法。基于某些非线性部分差异方程式与前向后向前向随机差异方程式之间的根本关系,我们制定了可扩展并适用于一般类随机系统以及机器人和自主决策问题配方的控制框架。拟议的用于随机控制的深神经网络结构由经常性和完全相连的层组成。上述算法的性能和可扩展性在三个非线性系统中进行模拟和无控制限制的调查。我们最后讨论了未来方向及其对机器人的影响。