Stochastic control for linear systems driven by fractional noises

CORC > 武汉物理与数学研究所 > 中国科学院武汉物理与数学研究所 > 2011年以前论文发表（包括2011年）

	Stochastic control for linear systems driven by fractional noises
	Hu, YZ ; Zhou, XY
刊名	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
	2005
卷号	43 期号:6 页码:2245-2277
关键词	fractional Brownian motion (FBM) stochastic linear-quadratic (LQ) control Ito integral Stratonovich integral Hu-Meyer formula multiple integral Riccati equation Malliavin derivative
英文摘要	This paper is concerned with optimal control of stochastic linear systems involving fractional Brownian motion (FBM). First, as a prerequisite for studying the underlying control problems, some new results on stochastic integrals and stochastic differential equations associated with FBM are established. Then, three control models are formulated and studied. In the first two models, the state is scalar-valued and the control is taken as Markovian. Either the problems are completely solved based on a Riccati equation (for model 1, where the cost is a quadratic functional on state and control variables) or optimality is characterized (for model 2, where the cost is a power functional). The last control model under investigation is a general one, where the system involves the Stratonovich integral with respect to FBM, the state is multidimensional, and the admissible controls are not limited to being Markovian. A new Riccati-type equation, which is a backward stochastic differential equation involving both FBM and normal Brownian motion, is introduced. Optimal control and optimal value of the model are explicitly obtained based on the solution to this Riccati-type equation.
WOS标题词	Science & Technology ; Technology ; Physical Sciences
类目[WOS]	Automation & Control Systems ; Mathematics, Applied
研究领域[WOS]	Automation & Control Systems ; Mathematics
关键词[WOS]	CONTROL WEIGHT COSTS ; BROWNIAN-MOTION ; DIFFERENTIAL-EQUATIONS ; QUADRATIC REGULATORS ; CALCULUS
收录类别	SCI
语种	英语
WOS记录号	WOS:000229826600018
公开日期	2015-07-28
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/4484]
专题	武汉物理与数学研究所_2011年以前论文发表（包括2011年）
作者单位	1.Univ Kansas, Dept Math, Lawrence, KS 66045 USA 2.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China 3.Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Hu, YZ,Zhou, XY. Stochastic control for linear systems driven by fractional noises[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2005,43(6):2245-2277.
APA	Hu, YZ,&Zhou, XY.(2005).Stochastic control for linear systems driven by fractional noises.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,43(6),2245-2277.
MLA	Hu, YZ,et al."Stochastic control for linear systems driven by fractional noises".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 43.6(2005):2245-2277.