This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of...This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of the solution process as well as of its expected value.Moreover,the cost functional is also of mean-field type.The control variable has two components,the first being absolutely continuous and the second singular.We establish necessary as well as sufficient conditions for optimal singular stochastic control where the system evolves according to MFSDEs.These conditions of optimality differs from the classical one in the sense that here the adjoint equation turns out to be a linear mean-field backward stochastic differential equation.The proof of our result is based on convex perturbation method of a given optimal control.The control domain is assumed to be convex.A linear quadratic stochastic optimal control problem of mean-field type is discussed as an illustrated example.展开更多
In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filter...In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation （GDRE）.展开更多
基金The authorwould like to thank the editor,the associate editor,and anonymous referees for their constructive corrections and valuable suggestions that improved the manuscript.The author was partially supported by Algerian PNR Project Grant 08/u07/857,ATRST-(ANDRU)2011-2013.
文摘This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of the solution process as well as of its expected value.Moreover,the cost functional is also of mean-field type.The control variable has two components,the first being absolutely continuous and the second singular.We establish necessary as well as sufficient conditions for optimal singular stochastic control where the system evolves according to MFSDEs.These conditions of optimality differs from the classical one in the sense that here the adjoint equation turns out to be a linear mean-field backward stochastic differential equation.The proof of our result is based on convex perturbation method of a given optimal control.The control domain is assumed to be convex.A linear quadratic stochastic optimal control problem of mean-field type is discussed as an illustrated example.
基金Supported by the National Natural Science Foundation of China (Grant No. 61174078)the Mathematical Tianyuan Youth Foundation of China (Grant No. 11126094)+1 种基金the Key Project of Natural Science Foundation of Shandong Province (Grant No. ZR2009GZ001)the research project of "SDUST Spring Bud" (Grant No.2009AZZ074)
文摘In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation （GDRE）.
