EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 35 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 35
Number of page(s) 45
DOI https://doi.org/10.1051/cocv/2025023
Published online 02 April 2025
  1. B.D.O. Anderson and J.B. Moore, Optimal Control: Linear Quadratic Methods. Dover (2007). [Google Scholar]
  2. T. Başar and G.J. Olsder, Dynamic Noncooperative Game Theory, 2nd edn. SIAM, Philadelphia (1999). [Google Scholar]
  3. A. Bensoussan, Estimation and Control of Dynamical Systems. Springer (2018). [Google Scholar]
  4. L.V.O. Costa, M.D. Fragoso and M.G. Todorov, Continuous-Time Markov Jump Linear Systems. Springer (2013). [Google Scholar]
  5. J. Engwerda, LQ Dynamic Optimization and Differential Games. Wiley (2005). [Google Scholar]
  6. J. Sun and J. Yong, Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions. Springer (2020). [Google Scholar]
  7. J. Yong, Differential Games: A Concise Introduction. World Scientific (2015). [Google Scholar]
  8. J. Yong and X.Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer (1999). [Google Scholar]
  9. J.M. Bismut, Linear–quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 14 (1976) 419–444. [CrossRef] [MathSciNet] [Google Scholar]
  10. Y. Hu and B. Oksendal, Partial information linear quadratic control for jump diffusions. SIAM J. Control Optim. 47 (2008) 1744–1761. [Google Scholar]
  11. Y. Jia, X. Feng, J. Huang and T. Xin, Robust backward linear–quadratic differential game and team: a soft-constraint analysis. Syst. Control Lett. 177 (2023) 1–12. [Google Scholar]
  12. H. Kushner, A partial history of the early development of continuous-time nonlinear stochastic systems theory. Automatica 50 (2014) 303–334. [Google Scholar]
  13. Q. Lü, Stochastic linear quadratic optimal control problems for mean-field stochastic evolution equations. ESAIM: Control Optim. Calc. Var. 26 (2020) 1–28. [Google Scholar]
  14. J. Moon, Linear–quadratic stochastic Stackelberg differential games for jump-diffusion systems. SIAM J. Control Optim. 59 (2021) 954–976. [MathSciNet] [Google Scholar]
  15. J. Moon, Linear–quadratic mean-field type Stackelberg differential games for stochastic jump-diffusion systems. Math. Control Related Fields 12 (2022) 371–404. [Google Scholar]
  16. J. Sun, X. Li and J. Yong, Open-loop and closed-loop solvabilities for stochastic linear–quadratic optimal control problems. SIAM J. Control Optim. 5 (2016) 2274–2308. [Google Scholar]
  17. J. Sun and J. Yong, Linear–quadratic stochastic differential games: open-loop and closed-loop saddle point. SIAM J. Control Optim. 52 (2014) 4082–4121. [CrossRef] [MathSciNet] [Google Scholar]
  18. S. Tang and X. Li, Dynamic programming for general linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 53 (2015) 1082–1106. [CrossRef] [MathSciNet] [Google Scholar]
  19. W.M. Wonham, On a matrix Riccati equation of stochastic control. SIAM J. Control 6 (1968) 681–697. [CrossRef] [MathSciNet] [Google Scholar]
  20. F. Zhang, Y. Dong and Q. Meng, Backward stochastic Riccati equation with jumps associated with stochastic linear quadratic optimal control with jump and random coefficients. SIAM J. Control Optim. 58 (2020) 393–424. [CrossRef] [MathSciNet] [Google Scholar]
  21. X. Zhang, X. Li and J. Xiong, Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system. ESAIM: Control Optim. Calc. Var. 27 (2021) 1–35. [Google Scholar]
  22. X. Feng, Y. Hu and J. Huang, Linear–quadratic Stackelberg differential game: local information versus global information. https://hal.science/hal-03812039/document (2022). [Google Scholar]
  23. P. Huang, G. Wang and H. Zhang, A partial information linear–quadratic optimal control problem of backward stochastic differential equation with its applications. Sci. China Inform. Sci. 63 (2020) 1–13. [Google Scholar]
  24. Z. Li, D. Marelli, M. Fu, Q. Cai and W. Wang, Linear quadratic Gaussian Stackelberg game under asymmetric information patterns. Automatica 125 (2021) 1–7. [Google Scholar]
  25. Z. Li, D. Marelli, M. Fu and H. Zhang, LQG differential Stackelberg game under nested observation information patterns. IEEE Trans. Automatic Control 68 (2023) 5111–5118. [Google Scholar]
  26. T. Ma, J. Xu and H. Wang, LQ control of Itô stochastic system with asymmetric information. J. Math. Anal. Appl. 512 (2022) 1–12. [Google Scholar]
  27. J. Shi, G. Wang and J. Xiong, Leader-follower stochastic differential game with asymmetric information and applications. Automatica 63 (2016) 60–73. [Google Scholar]
  28. J. Shi, G. Wang and J. Xiong, Stochastic linear quadratic Stackelberg differential game with overlapping information. ESAIM: Control Optim. Calc. Var. 26 (2020) 1–38. [Google Scholar]
  29. G. Wang, Y. Wang and S. Zhang, An asymmetric information mean-field type linear–quadratic stochastic Stackelberg differential game with one leader and two followers. Optimal Control Appl. Methods 41 (2020) 1034–1051. [Google Scholar]
  30. 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, 2018. [CrossRef] [Google Scholar]
  31. S. Wu, Linear–quadratic non-zero sum backward stochastic differential game with overlapping information. IEEE Trans. Automatic Control 68 (2023) 1800–1806. [Google Scholar]
  32. Z. Wu and Y. Zhuang, Linear–quadratic partially observed forward-backward stochastic differential games and its application in finance. Appl. Math. Computat. 321 (2016) 577–592. [Google Scholar]
  33. Y. Zheng and J. Shi, Stackelberg stochastic differential game with asymmetric noisy observations. Int. J. Control 95 (2023) 2510–2530. [Google Scholar]
  34. Z. Yu, An optimal feedback control-strategy pair for zero-sum linear–quadratic stochastic differential game: the Riccati equation approach. SIAM J. Control Optim. 53 (2015) 2141–2167. [CrossRef] [MathSciNet] [Google Scholar]
  35. J. Wen, X. Li, J. Xiong and X. Zhang, Stochastic linear-quadratic optimal control problems with random coefficients and Markovian regime switching system. SIAM J. Control Optim. 61 (2023) 949–979. [MathSciNet] [Google Scholar]
  36. J. Moon, A sufficient condition for linear–quadratic stochastic zero-sum differential games for Markov jump systems. IEEE Trans. Automatic Control 64 (2019) 1619–1626. [Google Scholar]
  37. J. Sun, Two-person zero-sum stochastic linear–quadratic differential games. SIAM J. Control Optim. 59 (2021) 1804–1829. [MathSciNet] [Google Scholar]
  38. R.J. Elliot, L. Aggoun and J.B. Moore, Hidden Markov Models. Springer (1994). [Google Scholar]
  39. D. Applebaum, Lévy Processes and Stochastic Calculus, 2nd edn. Cambridge University Press, Cambridge (2009). [Google Scholar]
  40. B. Oksendal and A. Sulem, Applied Stochastic Control of Jump Diffusions, 2nd edn. Springer-Verlag, Heidelberg (2006). [Google Scholar]
  41. J. Moon, Backward reachability approach to state-constrained stochastic optimal control problem for jump-diffusion models. Adv. Continuous Discrete Models 68 (2022) 1–38. [Google Scholar]
  42. R. Durrett, Probability: Theory and Examples. Thomson Brooks/Cole (2005). [Google Scholar]
  43. X. Zhang, Z. Sun and J. Xiong. A general stochastic maximum principle for a Markov regime switching jump-diffusion model of mean-field type. SIAM J. Control Optim. 56 (2018) 2563–2592. [Google Scholar]
  44. R. Buckdahn, Y. Hu and J. Li, Stochastic representation for solutions of Isaacs’ type integral-partial differential equations. Stochast. Processes Appl. 121 (2011) 2715–2750. [Google Scholar]
  45. R. Buckdahn, P. Cardaliaguet and C. Rainer, Nash equilibrium payoffs for nonzero-sum stochastic differential games. SIAM J. Control Optim. 43 (2004) 624–642. [CrossRef] [MathSciNet] [Google Scholar]
  46. R.A. Horn and C.R. Johnson, Matrix Analysis, 2nd edn. Cambridge University Press, New York (2013). [Google Scholar]
  47. J. Sun, Mean-field stochastic linear quadratic optimal control problems: Open-loop solvabilities. ESAIM: Control Optim. Calc. Var. 23 (2017) 1099–1127. [MathSciNet] [Google Scholar]
  48. J. Moon, Linear–quadratic stochastic leader–follower differential games for Markov jump-diffusion models. Automatica 147 (2023) 1–41. [Google Scholar]
  49. T. Başar and P. Bernhard, H∞ Optimal Control and Related Minimax Design Problems, 2nd edn. Birkhäuser, Boston, MA (1995). [Google Scholar]
  50. M.C. Delfour, Linear quadratic differential games: saddle point and Riccati differential equation. SIAM J. Control Optim. 46 (2007) 750–774. [Google Scholar]
  51. J. Moon and Y. Kim, Linear exponential quadratic control for mean field stochastic systems. IEEE Trans. Automatic Control 64 (2019) 5094–5100. [Google Scholar]
  52. J. Moon, Linear–quadratic mean field stochastic zero-sum differential games. Automatica 120 (2020) 1–10. [Google Scholar]
  53. H. Abou-Kandil, G. Freiling and G. Jank, Matrix Riccati Equations in Control and Systems Theory. Birkhauser (2003). [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.