摘要
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.
基金
supported by the NSF of China under grants 11471231,11221101,11231007,11301298 and 11401404
the PCSIRT under grant IRT 16R53 and the Chang Jiang Scholars Program from Chinese Education Ministry
the Fundamental Research Funds for the Central Universities in China under grant 2015SCU04A02
the NSFC-CNRS Joint Research Project under grant 11711530142。