Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/12205
Title: A stochastic maximum principle for delayed mean-field stochastic differential equations and its applications
Authors: Du, H
Huang, J 
Qin, Y
Keywords: Maximum principle
Mean-field equation
Stochastic delayed system
Stochastic optimal control
Issue Date: 2013
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on automatic control, 2013, v. 58, no. 12, 6517869, p. 3212-3217 How to cite?
Journal: IEEE transactions on automatic control 
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.
URI: http://hdl.handle.net/10397/12205
ISSN: 0018-9286
EISSN: 1558-2523
DOI: 10.1109/TAC.2013.2264550
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