对一般滤子情形下SLQ问题最优反馈的刻画

控制论中的一个基本问题是为系统设计反馈最优控制.这已在LQ问题中得到了很好的实现.但是,在已有的文献中,对这一问题的随机情形的讨论多集中在自然滤子情形.本文应用转置解这一概念在一般滤子情形下给出了带随机系数的SLQ问题最优反馈控制存在的充分条件,证明了对一维控制问题而言这还是必要条件.

Characterization of Optimal Feedback for SLQ with General Filtration

One of the fundamental issues in Control Theory is to design feedback controls. Which is well achieved in the case of linear quadratic control problems. To date, the study of this problem in the stochastic setting is focused much on the natural filtration. In this paper, we utilize the notion of transposition solution to give a sufficient condition for the existence of an optimal feedback control for the stochastic linear quadratic control problems with random coefficients in the general filtration setting, and show it is also necessary for 1-dimensional system.