Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems

Jingrui Sun, Xun Li, Jiongmin Yong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

118 Citations (Scopus)


This paper is concerned with a stochastic linear quadratic (LQ) optimal control problem. The notions of open-loop and closed-loop solvabilities are introduced. A simple example shows that these two solvabilities are different. Closed-loop solvability is established by means of solvability of the corresponding Riccati equation, which is implied by the uniform convexity of the quadratic cost functional. Conditions ensuring the convexity of the cost functional are discussed, including the issue of how negative the control weighting matrix-valued function R(•) can be. Finiteness of the LQ problem is characterized by the convergence of the solutions to a family of Riccati equations. Then, a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. Finally, some illustrative examples are presented.
Original languageEnglish
Pages (from-to)2274-2308
Number of pages35
JournalSIAM Journal on Control and Optimization
Issue number5
Publication statusPublished - 1 Jan 2016


  • Closed-loop solvability
  • Finiteness
  • Linear quadratic optimal control
  • Open-loop solvability
  • Riccati equation
  • Stochastic differential equation

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


Dive into the research topics of 'Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems'. Together they form a unique fingerprint.

Cite this