Stochastic Linear Quadratic Optimal Control Problem: From Discrete to Continuous Time

摘要

This paper deals with the continuous-time stochastic LQ problem involving state and control dependent noises and its discrete-time counterparts, Given the unique solvability of the continuous-time LQ problem, it is shown that time-discrete LQ problems admit solutions in cases where the step-size is sufficiently small. Moreover, the author reveals the natural connections between them and makes it possible to approximate the original continuous-time LQ problem with a proper order by a sequence of discrete-time ones. Besides, based on the optimal control of the continuous (discrete)-time LQ problem, optimal controls for the associated discrete (continuous)- time LQ problem and demonstrate their asymptotic optimality are constructed.