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Characterization of optimal feedback for stochastic linear quadratic control problems
School of Mathematics, Sichuan University, Chengdu 610064, Sichuan Province, China |
References:
[1] |
Ait Rami, M, Moore, JB, Zhou, X:Indefinite stochastic linear quadratic control and generalized differential Riccati equation. SIAM J. Control Optim 40, 1296-1311 (2001) |
[2] |
Athans, M:The role and use of the stochastic linear-quadratic-Gaussian problem in control system design.IEEE Trans. Automat. Control 16, 529-552 (1971) |
[3] |
Ben-Israel, A, Greville, TNE:Generalized Inverses:Theory and Applications. Pure and Applied Mathematics. Wiley-Interscience[John Wiley & Sons], New York-London-Sydney (1974) |
[4] |
Bensoussan, A:Lectures on stochastic control. In:Nonlinear Filtering and Stochastic Control. Lecture Notes in Math, vol. 972, pp. 1-62. Springer-Verlag, Berlin (1981) |
[5] |
Bismut, J-M:Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim 14, 419-444 (1976) |
[6] |
Bismut, J-M:Contrôle des systèmes linéaires quadratiques:applications de l'intégrale stochastique. In:Séminaire de Probabilités XII, Université de Strasbourg 1976/77, Lecture Notes in Math, vol. 649, pp. 180-264. Springer-Verlag, Berlin (1978) |
[7] |
Briand, PH, Delyon, B, Hu, Y, Pardoux, E, Stoica, L:Lp solutions of backward stochastic differential equations. Stochastic Process. Appl 108, 109-129 (2003) |
[8] |
Chen, S, Li, X, Zhou, X:Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J. Control Optim 36, 1685-1702 (1998) |
[9] |
Davis, MHA:Linear Estimation and Stochastic Control. Chapman and Hall Mathematics Series. Chapman and Hall, London; Halsted Press[John Wiley & Sons], New York (1977) |
[10] |
Delbaen, F, Tang, S:Harmonic analysis of stochastic equations and backward stochastic differential equations. Probab. Theory Relat. Fields 146, 291-336 (2010) |
[11] |
Frei, C, dos Reis, G:A financial market with interacting investors:does an equilibrium exist? Math. Finan.Econ 4, 161-182 (2011) |
[12] |
Kalman, RE:Contributions to the theory of optimal control. Bol. Soc. Mat. Mexicana 5, 102-119 (1960) |
[13] |
Lü, Q, Zhang, X:Well-posedness of backward stochastic differential equations with general filtration. J. Diff. Equations 254, 3200-3227 (2013) |
[14] |
Lü, Q, Zhang, X:General Pontryagin-Type Stochastic Maximum Principle and Backward StochasticEvolution Equations in Infinite Dimensions. Springer Briefs in Mathematics. Springer, Cham (2014) |
[15] |
Lü, Q, Zhang, X:Transposition method for backward stochastic evolution equations revisited, and its application. Math. Control Relat. Fields 5, 529-555 (2015) |
[16] |
Lü, Q, Zhang, X:Optimal feedback for stochastic linear quadratic control and backward stochastic Riccati equations in infinite dimensions. (2017). Preprint Pardoux, E, Peng, S:Adapted solution of backward stochastic equation. Systems Control Lett 14, 55-61(1990) |
[17] |
Peng, S:Stochastic Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim 30, 284-304 (1992) |
[18] |
Pham, H:Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications. (2017). arXiv:1604.06609v1 |
[19] |
Protter, PE:Stochastic Integration and Differential Equations. Stochastic Modelling and Applied Probability, vol. 21. Springer-Verlag, Berlin (2005) |
[20] |
Reid, WT:A matrix differential equation of Riccati type. Amer. J. Math 68, 237-246 (1946) |
[21] |
Sun, J, Yong, J:Linear quadratic stochastic differential games:open-loop and closed-loop saddle points.SIAM J. Control Optim 52, 4082-4121 (2014) |
[22] |
Tang, S:General linear quadratic optimal stochastic control problems with random coefficients:linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim 42, 53-75 (2003) |
[23] |
Tang, S:Dynamic programming for general linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim 53, 1082-1106 (2015) |
[24] |
Wonham, WM:On a matrix Riccati equation of stochastic control. SIAM J. Control 6, 681-697 (1968) |
[25] |
Wonham, WM:Linear Multivariable Control, a Geometric Approach. Applications of Mathematics, vol. 10. Springer-Verlag, New York (1985) |
[26] |
Yong, J, Lou, H:A Concise Course on Optimal Control Theory. Higher Education Press, Beijing (2006).(In Chinese) |
[27] |
Yong, J, Zhou, XY:Stochastic Controls:Hamiltonian Systems and HJB Equations. Springer-Verlag, New York, Berlin (2000) |
show all references
References:
[1] |
Ait Rami, M, Moore, JB, Zhou, X:Indefinite stochastic linear quadratic control and generalized differential Riccati equation. SIAM J. Control Optim 40, 1296-1311 (2001) |
[2] |
Athans, M:The role and use of the stochastic linear-quadratic-Gaussian problem in control system design.IEEE Trans. Automat. Control 16, 529-552 (1971) |
[3] |
Ben-Israel, A, Greville, TNE:Generalized Inverses:Theory and Applications. Pure and Applied Mathematics. Wiley-Interscience[John Wiley & Sons], New York-London-Sydney (1974) |
[4] |
Bensoussan, A:Lectures on stochastic control. In:Nonlinear Filtering and Stochastic Control. Lecture Notes in Math, vol. 972, pp. 1-62. Springer-Verlag, Berlin (1981) |
[5] |
Bismut, J-M:Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim 14, 419-444 (1976) |
[6] |
Bismut, J-M:Contrôle des systèmes linéaires quadratiques:applications de l'intégrale stochastique. In:Séminaire de Probabilités XII, Université de Strasbourg 1976/77, Lecture Notes in Math, vol. 649, pp. 180-264. Springer-Verlag, Berlin (1978) |
[7] |
Briand, PH, Delyon, B, Hu, Y, Pardoux, E, Stoica, L:Lp solutions of backward stochastic differential equations. Stochastic Process. Appl 108, 109-129 (2003) |
[8] |
Chen, S, Li, X, Zhou, X:Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J. Control Optim 36, 1685-1702 (1998) |
[9] |
Davis, MHA:Linear Estimation and Stochastic Control. Chapman and Hall Mathematics Series. Chapman and Hall, London; Halsted Press[John Wiley & Sons], New York (1977) |
[10] |
Delbaen, F, Tang, S:Harmonic analysis of stochastic equations and backward stochastic differential equations. Probab. Theory Relat. Fields 146, 291-336 (2010) |
[11] |
Frei, C, dos Reis, G:A financial market with interacting investors:does an equilibrium exist? Math. Finan.Econ 4, 161-182 (2011) |
[12] |
Kalman, RE:Contributions to the theory of optimal control. Bol. Soc. Mat. Mexicana 5, 102-119 (1960) |
[13] |
Lü, Q, Zhang, X:Well-posedness of backward stochastic differential equations with general filtration. J. Diff. Equations 254, 3200-3227 (2013) |
[14] |
Lü, Q, Zhang, X:General Pontryagin-Type Stochastic Maximum Principle and Backward StochasticEvolution Equations in Infinite Dimensions. Springer Briefs in Mathematics. Springer, Cham (2014) |
[15] |
Lü, Q, Zhang, X:Transposition method for backward stochastic evolution equations revisited, and its application. Math. Control Relat. Fields 5, 529-555 (2015) |
[16] |
Lü, Q, Zhang, X:Optimal feedback for stochastic linear quadratic control and backward stochastic Riccati equations in infinite dimensions. (2017). Preprint Pardoux, E, Peng, S:Adapted solution of backward stochastic equation. Systems Control Lett 14, 55-61(1990) |
[17] |
Peng, S:Stochastic Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim 30, 284-304 (1992) |
[18] |
Pham, H:Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications. (2017). arXiv:1604.06609v1 |
[19] |
Protter, PE:Stochastic Integration and Differential Equations. Stochastic Modelling and Applied Probability, vol. 21. Springer-Verlag, Berlin (2005) |
[20] |
Reid, WT:A matrix differential equation of Riccati type. Amer. J. Math 68, 237-246 (1946) |
[21] |
Sun, J, Yong, J:Linear quadratic stochastic differential games:open-loop and closed-loop saddle points.SIAM J. Control Optim 52, 4082-4121 (2014) |
[22] |
Tang, S:General linear quadratic optimal stochastic control problems with random coefficients:linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim 42, 53-75 (2003) |
[23] |
Tang, S:Dynamic programming for general linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim 53, 1082-1106 (2015) |
[24] |
Wonham, WM:On a matrix Riccati equation of stochastic control. SIAM J. Control 6, 681-697 (1968) |
[25] |
Wonham, WM:Linear Multivariable Control, a Geometric Approach. Applications of Mathematics, vol. 10. Springer-Verlag, New York (1985) |
[26] |
Yong, J, Lou, H:A Concise Course on Optimal Control Theory. Higher Education Press, Beijing (2006).(In Chinese) |
[27] |
Yong, J, Zhou, XY:Stochastic Controls:Hamiltonian Systems and HJB Equations. Springer-Verlag, New York, Berlin (2000) |
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