论文标题
非线性过滤的二元性II：最佳控制
Duality for Nonlinear Filtering II: Optimal Control
论文作者
论文摘要
本文涉及对二元理论的发展和使用，用于具有白噪声观察的非线性过滤模型。本文的主要贡献是引入一个随机的最佳控制问题，作为非线性滤波问题的双重。这两个问题之间双重关系的数学陈述是以双重性原理的形式给出的。最佳控制问题的限制是伴侣论文中引入的向后随机微分方程（BSDE）。最佳控制解决方案是从最大原理的应用中获得的，随后用于得出非线性滤波器的方程。所提出的二元性被证明是经典的卡尔曼 - 兼二元性的确切扩展，并且与文献中给出的其他最佳控制和变异表述不同。
This paper is concerned with the development and use of duality theory for a nonlinear filtering model with white noise observations. The main contribution of this paper is to introduce a stochastic optimal control problem as a dual to the nonlinear filtering problem. The mathematical statement of the dual relationship between the two problems is given in the form of a duality principle. The constraint for the optimal control problem is the backward stochastic differential equation (BSDE) introduced in the companion paper. The optimal control solution is obtained from an application of the maximum principle, and subsequently used to derive the equation of the nonlinear filter. The proposed duality is shown to be an exact extension of the classical Kalman-Bucy duality, and different from other types of optimal control and variational formulations given in literature.
