On the LQG theory with bounded control

  • D. V. Iourtchenko
  • J. L. Menaldi
  • A. S. Bratus


We consider a stochastic optimal control problem in the whole space, where the corresponding HJB equation is degenerate, with a quadratic running cost and coefficients with a linear growth. In this paper we provide full mathematical details on the key estimate relating the asymptotic behavior of the solution as the space variables tend to infinite.

Mathematics Subject Classification (2000)

Primary 93E20 Secondary 49J15 


Optimal control Stochastic control Hamilton-Jacobi-Bellman equation Asymptotic behavior 


  1. 1.
    Bardi, M., Capuzzo-Dolcetta, I.: Optimal control and viscosity solutions of Hamilton–Jacobi–Bellman equations. Birkhäuser (1997)Google Scholar
  2. 2.
    Bratus A.S., Iourtchenko D.V., Menaldi J.-L.: Local solutions to the Hamilton–Jacobi–Bellman equation in stochastic problems of optimal control. Dokl. Math. 74(1), 610–613 (2006)CrossRefzbMATHGoogle Scholar
  3. 3.
    Crandall M.G., Lions P.L.: Viscosity solutions of Hamilton–Jacobi equations. Trans. Am. Math. Soc. 277, 1–42 (1984)MathSciNetGoogle Scholar
  4. 4.
    Dreyfus S.E.: Dynamic Programming and Calculus of Variations. Academic Press, New York (1965)zbMATHGoogle Scholar
  5. 5.
    Fleming W.H., Soner H.M.: Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York (1992)Google Scholar
  6. 6.
    Iourtchenko D.V.: Solution to a class of stochastic LQ problems with bounded control. Automatica 45, 1439–1442 (2009)CrossRefzbMATHGoogle Scholar
  7. 7.
    Krylov N.V.: Controlled Diffusion Processes. Springer-Verlag, Berlin (1980)zbMATHGoogle Scholar

Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  • D. V. Iourtchenko
    • 1
  • J. L. Menaldi
    • 2
  • A. S. Bratus
    • 3
  1. 1.Department of Mathematical SciencesSaint-Petersburg State Polytechnic UniversitySaint-PetersburgRussia
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA
  3. 3.Department of MathematicsMIITMoscowRussia

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