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Stochastic linear quadratic optimal control problem: from discrete to continuous time. (Chinese. English summary) Zbl 1424.49022

Summary: 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 their asymptotic optimality are constructed.

MSC:

49J55 Existence of optimal solutions to problems involving randomness
49N05 Linear optimal control problems
49M25 Discrete approximations in optimal control
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