唐雷
（山东科技大学，山东 青岛 266590）
【摘要】研究了一类特殊的线性正倒向随机控制系统的最优控制问题，通过运用最大值原理来解决所给出的线性二次随机最优控制问题，从而获得线性二次指标泛函下的控制的显示形式，并验证了控制的显示表达式是最优控制并且唯一。
教育期刊网 http://www.jyqkw.com
关键词 线性二次正倒向随机控制系统；随机最优控制；随机最大值原理
One kind of Linear Quadratic Forward-Backward Stochastic Optimal Control Problem
TANG Lei
(Shandong University of sciense and Technology, Qingdao Shandong 266590, China)
【Abstract】We study one kind of linear quadratic forward-backward stochastic optimal problems,and get the explicit accurate form of the optimal control for the linear quadratic stochastic optimal problem by stochastic maximum principle.Finally,we proved that the control is the optimal control and the unique.
【Key words】Linear quadratic stochastic control system; Optimal control; Stochastic maximum principle
0引言
教育期刊网 http://www.jyqkw.com
参考文献
［１］Wu Zhen. Maximum Principle for Optimal Control Problem of Fully Coupled Forward-Backward Stochastic Systems[J]. System Science and Mathematical Science,1998,11(3).
［２］Wang, X.R，Gao,Z.Y，Wu,Z.:Forward-Backward Stochastic Differential Equation and the Liner Quadratic Stochastic Optimal Control[J]. ACTA AUTOMATICA SINICA，2003,29(1):32-37.
［３］肖华,吴臻．一类线性二次正倒向随机最优控制系统的最优控制问题[C]//程代展,王行愚．第二十三届中国控制会议论文集.上海∶华东理工大学出版社,2004:99-103．
［４］Pontryagin L S. Boltyanskii B T. Gamkrelidze R V，Mishchenko E F. The Mathematical Theory of Optimal Processes[M]. New York：Interscience，1962.
［５］Bensoussan A. Lectures in stochastic control. In：Proceedings Cortona，Lecture Notes in Mathematics[M]. New York：Springer,1981,972(1):1-62.
［责任编辑：汤静］
