Solvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems

Jianhui Huang, Zhiyong Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)


A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the "equivalent cost functional method", is introduced by Yu (2013) in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefinite stochastic Riccati equations. As the response, this paper continues to develop the equivalent cost functional method by extending it to the Riccati equation setup. Our analysis is featured by its introduction of some equivalent cost functionals which enable us to have the bridge between the indefinite and positive-definite stochastic LQ problems. With such bridge, some solvability relation between the indefinite and positive-definite Riccati equations is further characterized. It is remarkable the solvability of the former is rather complicated than the latter, hence our relation provides some alternative but useful viewpoint. Consequently, the corresponding indefinite linear quadratic problem is discussed for which the unique optimal control is derived in terms of state feedback via the solution of the Riccati equation. In addition, some example is studied using our theoretical results.
Original languageEnglish
Pages (from-to)68-75
Number of pages8
JournalSystems and Control Letters
Issue number1
Publication statusPublished - 1 Jun 2014


  • Backward stochastic differential equation (BSDE)
  • Stochastic linear quadratic optimal control
  • Stochastic Riccati equation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • General Computer Science
  • Mechanical Engineering


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