Paper Info
Title
A Stochastic Maximum Principle for Delayed Mean-Field Stochastic Differential Equations and Its Applications
Abstract
In this technical note, we discuss the stochastic optimal control problems of mean-field stochastic differential delayed equations (MFSDDEs) which arise naturally from various backgrounds including economics, finance, engineering and physics, etc. To this end, some new estimates are used to handle the complex structure of our controlled system due to the presence of both delay and mean-field characters. As the main result, a stochastic maximum principle for the mean-field stochastic optimal control with delay (MFSOCD) is derived in terms of necessary and sufficient conditions. In particular, applying the convex variation and duality relation, we obtain the necessary condition for optimality (see Theorem 1). In addition, the sufficient condition of the optimality is also obtained under some convex condition (see Theorem 2). Based on our maximum principle, the related mean-field linear quadratic delayed (MFLQD) optimal control problems are also investigated. The optimal control is derived and its existence is also verified (refer Theorem 3). As illustration, an example is also proposed and its explicit optimal control is derived.
Year
DOI
Venue
2013
10.1109/TAC.2013.2264550
IEEE Trans. Automat. Contr.
Keywords
Field
DocType
Optimal control,Delays,Equations,Aerospace electronics,Stochastic processes,Adaptation models
Mathematical optimization,Stochastic optimization,Maximum principle,Optimal control,Separation principle,Control theory,Stochastic calculus,Continuous-time stochastic process,Stochastic partial differential equation,Mathematics,Stochastic control
Journal
Volume
Issue
ISSN
58
12
0018-9286
Citations 
PageRank 
References 
4
0.57
7
Authors
3
Name
Order
Citations
PageRank
Heng Du151.84
Jianhui Huang28114.20
Yongli Qin340.57