A stochastic maximum principle for delayed mean-field stochastic differential equations and its applications

Heng Du, Jianhui Huang, Yongli Qin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)


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.
Original languageEnglish
Article number6517869
Pages (from-to)3212-3217
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number12
Publication statusPublished - 1 Dec 2013


  • Maximum principle
  • Mean-field equation
  • Stochastic delayed system
  • Stochastic optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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