Chinese Annals of Mathematics,Series B, Volume. 46, Issue 4, 583(2025)
Stochastic Linear Quadratic Optimal Control Problems for Stochastic Evolution Equations with Unbounded Control Operator
[1] [1] Bensoussan, A., Lectures on Stochastic Control, Nonlinear Filtering and Stochastic Control (CIME Proceedings, Cortona, Italy 1981), Lecture Notes in Mathematics,972, Springer-Verlag, Berlin, 1982, 1–62.
[2] [2] Bensoussan, A., Da Prato, G., Delfour, M. C. and Mitter, S. K., Representation and Control of Infinite Dimensional Systems, Birkhuser Boston, Inc., Boston, MA, 1993.
[3] [3] Chen, S., Li, X. and Zhou, X., Stochastic linear quadratic regulators with indefinite control weight costs,SIAM J. Control Optim.,36, 1998, 1685–1702.
[4] [4] Chen, S. and Yong, J., Stochastic linear quadratic optimal control problems,Appl. Math. Optim.,43, 2001, 21–45.
[5] [5] Chen, S. and Zhou, X., Stochastic linear quadratic regulators with indefinite control weight costs. II,SIAM J. Control Optim.,39, 2000, 1065–1081.
[6] [6] Curtain, R. F. and Ichikawa, A., The separation principle for stochastic evolution equations,SIAM J. Control Optim.,15, 1977, 367–383.
[7] [7] Davis, M. H. A., Linear Estimation and Stochastic Control, Chapman and Hall, London, 1977.
[8] [8] Dou, F. and L, Q., Time-inconsistent linear quadratic optimal control problems for stochastic evolution equations,SIAM J. Control Optim.,58, 2020, 485–509.
[9] [9] Guatteri, G. and Tessitore, G., On the backward stochastic Riccati equation in infinite dimensions,SIAM J. Control Optim.,44, 2005, 159–194.
[10] [10] Hafizoglu, C., Lasiecka, I., Levajkovic, T., et al., The stochastic linear quadratic control problem with singular estimates,SIAM J. Control Optim.,55, 2017, 595–626.
[11] [11] Hu, Y. and Zhou, X., Indefinite stochastic Riccati equations,SIAM J. Control Optim.,42, 2003, 123–137.
[12] [12] Kotelenez, P., Stochastic Ordinary and Stochastic Partial Differential Equations, Transition from Microscopic to Macroscopic Equations, Springer-Verlag, New York, 2008.
[13] [13] Lasiecka, I., Mathematical Control Theory of Coupled PDEs, CBM-NSF Regional Conf. Ser.in App. Math.,75, SIAM, Philadelphia, 2002.
[14] [14] L, Q., Stochastic well-posed systems and well-posedness of some stochastic partial differential equations with boundary control and observation,SIAM J. Control Optim.,53, 2015, 3457–3482.
[15] [15] L, Q., Well-posedness of stochastic Riccati equations and closed-loop solvability for stochastic linear quadratic optimal control problems,J. Differential Equations,267, 2019, 180–227.
[16] [16] L, Q., Stochastic linear quadratic optimal control problems for mean-field stochastic Evolution equations,ESAIM Control Optim. Calc. Var.,26, 2020, 1–28.
[17] [17] L, Q. and Zhang, X., Mathematical Control Theory for Stochastic Partial Differential Equations, Probab. Theory Stoch. Model.101, Springer-Verlag, Switzerland AG, 2021.
[18] [18] Sun, J. and Yong, J., Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions, Springer-Verlag, Cham, 2020.
[19] [19] Sun, J. and Yong, J., Stochastic Linear-quadratic Optimal Control Theory: Differential Games and Meanfield Problems, Springer-Verlag, Cham, 2020.
[20] [20] Wu, H. and Li, X., A linear quadratic problem with unbounded control in Hilbert spaces,Differ. Integral Equ.,13, 2000, 529–566.
[21] [21] Yong, J. and Zhou, X., Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999.
Get Citation
Copy Citation Text
WANG Yan. Stochastic Linear Quadratic Optimal Control Problems for Stochastic Evolution Equations with Unbounded Control Operator[J]. Chinese Annals of Mathematics,Series B, 2025, 46(4): 583
Received: Sep. 16, 2022
Accepted: Aug. 25, 2025
Published Online: Aug. 25, 2025
The Author Email: