二次性能指标下的随机控制问题

<正> 随机控制中的二次性能指标是一种十分重要的情况,对离散时间并对状态是线性的系统,问题已得到彻底解决.对连续时间系统,也已多有讨论,但迄今给出的证明还并不完满,所要求的条件也太强. 设(Ω,,P)是概率空间,{},0≤t≤T是以中的零测集完备了的非降

STOCHASTIC CONTROL PROBLEM WITH THE QUADRATIC PERFORMANCE INDEX

The results obtained so far on the stochastic control under the quadratic index are discussed in this paper and at the same time their defects are pointed out. To avoid these defects, the unique condition imposed on the matrix coefficients of the system is their integrability in some sense, and a suitable set of admissible controls is now selected. In this paper the existence and the uniqueness of solution of a Riccati equation are considered and the existent nonlinear filtering equation is rewritten into a form which we need. By means of these results for the linear stochastic systemwith the quadratic index the separation principle is proved and the optimal controlis given.