Forward-backward linear quadratic stochastic optimal control problem with delay

Jianhui Huang, Xun Li, Jingtao Shi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

34 Citations (Scopus)


This paper is concerned with one kind of forward-backward linear quadratic stochastic control problem whose system is described by a linear anticipated forward-backward stochastic differential delayed equation. The explicit form of the optimal control is derived. Optimal state feedback regulators are studied in two special cases. For the case with delay in just the control variable, the optimal state feedback regulator is obtained by the Riccati equation. For the other case with delay in just the state variable, the optimal state feedback regulator is analyzed by the value function approach.
Original languageEnglish
Pages (from-to)623-630
Number of pages8
JournalSystems and Control Letters
Issue number5
Publication statusPublished - 1 May 2012


  • Anticipated backward stochastic differential equation
  • Linear quadratic control
  • Stochastic delayed system
  • Stochastic differential delayed equation
  • Stochastic optimal control
  • Time-inconsistent

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)
  • Mechanical Engineering
  • Electrical and Electronic Engineering

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