Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 35
Number of page(s) 30
DOI https://doi.org/10.1051/cocv/2023033
Published online 24 May 2023
  1. A. Bensoussan, Lectures on stochastic control, part I, in Nonlinear Filtering and Stochastic Control, Lecture Notes in Math. 972, Springer-Verlag, Berlin (1982), 1–39. [Google Scholar]
  2. X. Bi, J. Sun and J. Xiong, Optimal control for controllable stochastic linear systems. ESAIM-Control Optim. Calc. Var. 26 (2020) 98. [Google Scholar]
  3. S. Chen, X. Li and X.Y. Zhou, Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J. Control Optim. 36 (1998) 1685–1702. [Google Scholar]
  4. S. Chen and J. Yong, Stochastic linear quadratic optimal control problems. Appl. Math. Optim. 43 (2001) 21–45. [Google Scholar]
  5. S. Chen and X.Y. Zhou, Stochastic linear quadratic regulators with indefinite control weight costs. II. SIAM J. Control Optim. 39 (2000) 1065–1081. [Google Scholar]
  6. M.H.A. Davis, Linear Estimation and Stochastic Control. Chapman and Hall, London (1977). [Google Scholar]
  7. K. Du, Solvability conditions for indefinite linear quadratic optimal stochastic control problems and associated stochastic Riccati equations. SIAM J. Control Optim. 53 (2015) 3673–3689. [Google Scholar]
  8. K. Du, J. Huang and Z. Wu, Linear quadratic mean-field-game of backward stochastic differential systems, Math. Control Relat. Fields 8 (2018) 653–678. [CrossRef] [MathSciNet] [Google Scholar]
  9. J. Huang, X. Li and J. Shi, Forward-backward linear quadratic stochastic optimal control problem with delay. Syst. Control. Lett. 61 (2012) 623–630. [Google Scholar]
  10. J. Huang, S. Wang and Z. Wu, Backward mean-field linear-quadratic-Gaussian (LQG) games: full and partial information. IEEE Trans. Automat. Control 61 (2016) 3784–3796. [CrossRef] [MathSciNet] [Google Scholar]
  11. N. Li, Z. Wu and Z. Yu, Indefinite stochastic linear-quadratic optimal control problems with random jumps and related stochastic Riccati equations. Sci. ChinaMath. 61 (2018) 563–576. [Google Scholar]
  12. X. Li, J. Sun and J. Xiong, Linear quadratic optimal control problems for mean-field backward stochastic differential equations. Appl. Math. Optim. 80 (2019) 223–250. [Google Scholar]
  13. A.E.B. Lim and X.Y. Zhou, Linear-quadratic control of backward stochastic differential equations. SIAM J. Control Optim. 40 (2001) 450–474. [Google Scholar]
  14. Q. Lu, T. Wang and X. Zhang, Characterization of optimal feedback for stochastic linear quadratic control problems. Probab. Uncertain. Quant. Risk 2 (2017) 11. [CrossRef] [Google Scholar]
  15. J. Ma and J. Yong, Forward-Backward Stochastic Differential Equations and Their Applications, Lecture Notes in Math. 1702. Springer-Verlag, New York (1999). [Google Scholar]
  16. S. Peng, Backward stochastic differential equation, nonlinear expectation and their applications, in Proceedings of the International Congress of Mathematicians, Vol. I (2010), 393–432. [Google Scholar]
  17. H. Pham, Continuous-Time Stochastic Control and Optimization with Financial Applications. Springer-Verlag, Berlin (2009). [CrossRef] [Google Scholar]
  18. J. Sun, X. Li and J. Yong, Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems. SIAM J. Control Optim. 54 (2016) 2274–2308. [Google Scholar]
  19. J. Sun and H. Wang, Linear-quadratic optimal control for backward stochastic differential equations with random coefficients. ESAIM-Control Optim. Calc. Var. 27 (2021) 46. [Google Scholar]
  20. J. Sun, J. Wen and J. Xiong, General indefinite backward stochastic linear-quadratic optimal control problems. ESAIM-Control Optim. Calc. Var. 28 (2022) 35. [Google Scholar]
  21. J. Sun, Z. Wu and J. Xiong, Indefinite backward stochastic linear-quadratic optimal control problems. arXiv:2104.04747 (2021). [Google Scholar]
  22. J. Sun, J. Xiong and J. Yong, Indefinite stochastic linear-quadratic optimal control problems with random coefficients: closed- loop representation of open-loop optimal controls. Ann. Appl. Probab. 31 (2021) 460–499. [Google Scholar]
  23. J. Sun and J. Yong, Linear quadratic stochastic differential games: open-loop and closed-loop saddle points. SIAM J. Control Optim. 52 (2014) 4082–4121. [Google Scholar]
  24. J. Sun and J. Yong, Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions. SpringerBriefs in Mathematics. Springer, Cham (2020). [Google Scholar]
  25. J. Sun and J. Yong, Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems. SpringerBriefs in Mathematics. Springer, Cham (2020). [Google Scholar]
  26. G. Wang, Z. Wu and J. Xiong, Partial information LQ optimal control of backward stochastic differential equations, in Proceedings of the 10th World Congress on Intelligent Control and Automation, IEEE (2012) 1694–1697. [CrossRef] [Google Scholar]
  27. G. Wang, Z. Wu and J. Xiong, A linear-quadratic optimal control problem of forward-backward stochastic differential equations with partial information. IEEE Trans. Automat. Control 60 (2015) 2904–2916. [CrossRef] [MathSciNet] [Google Scholar]
  28. G. Wang, H. Xiao and G. Xing, An optimal control problem for mean-field forward-backward stochastic differential equation with noisy observation. Automatica 86 (2017) 104–109. [CrossRef] [Google Scholar]
  29. G. Wang, H. Xiao and J. Xiong, A kind of LQ non-zero sum differential game of backward stochastic differential equation with asymmetric information. Automatica 97 (2018) 346–352. [CrossRef] [Google Scholar]
  30. W.M. Wonham, On a matrix Riccati equation of stochastic control. SIAM J. Control 6 (1968) 681–697. [CrossRef] [MathSciNet] [Google Scholar]
  31. J. Yong, A leader-follower stochastic linear quadratic differential game. SIAM J. Control Optim. 41 (2002) 1015–1041. [Google Scholar]
  32. J. Yong, Differential Games – A Concise Introduction. World Scientific Publisher, Singapore (2015). [CrossRef] [Google Scholar]
  33. J. Yong and X.Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999). [Google Scholar]
  34. Z. Yu, Linear-quadratic optimal control and nonzero-sum differential game of forward-backward stochastic system. Asian J. Control 14 (2012) 173–185. [CrossRef] [MathSciNet] [Google Scholar]
  35. J. Zhang, Backward Stochastic Differential Equations: From Linear to Fully Nonlinear Theory. Springer-Verlag, New York (2017). [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.