In this work,the author proposes a discretization for stochastic linear quadratic control problems(SLQ problems)subject to stochastic differential equations.The author firstly makes temporal discretization and obtains...In this work,the author proposes a discretization for stochastic linear quadratic control problems(SLQ problems)subject to stochastic differential equations.The author firstly makes temporal discretization and obtains SLQ problems governed by stochastic difference equations.Then the author derives the convergence rates for this discretization relying on stochastic differential/difference Riccati equations.Finally an algorithm is presented.Compared with the existing results relying on stochastic Pontryagin-type maximum principle,the proposed scheme avoids solving backward stochastic differential equations and/or conditional expectations.展开更多
One of the fundamental issues in Control Theory is to design feedback controls.It is well-known that,the purpose of introducing Riccati equations in the study of deterministic linear quadratic control problems is exac...One of the fundamental issues in Control Theory is to design feedback controls.It is well-known that,the purpose of introducing Riccati equations in the study of deterministic linear quadratic control problems is exactly to construct the desired feedbacks.To date,the same problem in the stochastic setting is only partially well-understood.In this paper,we establish the equivalence between the existence of optimal feedback controls for the stochastic linear quadratic control problems with random coefficients and the solvability of the corresponding backward stochastic Riccati equations in a suitable sense.We also give a counterexample showing the nonexistence of feedback controls to a solvable stochastic linear quadratic control problem.This is a new phenomenon in the stochastic setting,significantly different from its deterministic counterpart.展开更多
基金This work was supported in part by the National Natural Science Foundation of China under Grant No.11801467the Chongqing Natural Science Foundation under Grant No.cstc2018jcyjAX0148.
文摘In this work,the author proposes a discretization for stochastic linear quadratic control problems(SLQ problems)subject to stochastic differential equations.The author firstly makes temporal discretization and obtains SLQ problems governed by stochastic difference equations.Then the author derives the convergence rates for this discretization relying on stochastic differential/difference Riccati equations.Finally an algorithm is presented.Compared with the existing results relying on stochastic Pontryagin-type maximum principle,the proposed scheme avoids solving backward stochastic differential equations and/or conditional expectations.
基金supported by the NSF of China under grants 11471231,11221101,11231007,11301298 and 11401404the PCSIRT under grant IRT 16R53 and the Chang Jiang Scholars Program from Chinese Education Ministry+1 种基金the Fundamental Research Funds for the Central Universities in China under grant 2015SCU04A02the NSFC-CNRS Joint Research Project under grant 11711530142。
文摘One of the fundamental issues in Control Theory is to design feedback controls.It is well-known that,the purpose of introducing Riccati equations in the study of deterministic linear quadratic control problems is exactly to construct the desired feedbacks.To date,the same problem in the stochastic setting is only partially well-understood.In this paper,we establish the equivalence between the existence of optimal feedback controls for the stochastic linear quadratic control problems with random coefficients and the solvability of the corresponding backward stochastic Riccati equations in a suitable sense.We also give a counterexample showing the nonexistence of feedback controls to a solvable stochastic linear quadratic control problem.This is a new phenomenon in the stochastic setting,significantly different from its deterministic counterpart.
