论文标题
随机汉密尔顿 - 雅各比 - 贝尔曼方程，路径积分和库普曼操作员在非线性随机最佳控制上
Connection among stochastic Hamilton-Jacobi-Bellman equation, path-integral, and Koopman operator on nonlinear stochastic optimal control
论文作者
论文摘要
源自随机的汉密尔顿 - 雅各比 - 贝尔曼方程的路径综合控制是控制随机非线性系统的方法之一。本文从Koopman运营商的角度对非线性随机最佳控制问题提供了新的见解。当有限维动力系统是非线性时，相应的Koopman操作员是线性的。尽管Koopman操作员是无限维度的，但适当的近似使其在某些讨论和应用中可进行且有用。采用Koopman操作员的角度，可以澄清说，只有一种特定类型的可观察到足以将重点放在控制问题中。通过路径综合控制，这一事实变得更容易理解。此外，对特定可观察到的专注于自然力量系列的扩展。得出了离散空间系统的耦合的普通微分方程。非线性随机最佳控制的演示表明，派生的方程式效果很好。
The path-integral control, which stems from the stochastic Hamilton-Jacobi-Bellman equation, is one of the methods to control stochastic nonlinear systems. This paper gives a new insight into nonlinear stochastic optimal control problems from the perspective of Koopman operators. When a finite-dimensional dynamical system is nonlinear, the corresponding Koopman operator is linear. Although the Koopman operator is infinite-dimensional, adequate approximation makes it tractable and useful in some discussions and applications. Employing the Koopman operator perspective, it is clarified that only a specific type of observable is enough to be focused on in the control problem. This fact becomes easier to understand via path-integral control. Furthermore, the focus on the specific observable leads to a natural power-series expansion; coupled ordinary differential equations for discrete-state space systems are derived. A demonstration for nonlinear stochastic optimal control shows that the derived equations work well.
