Abstract
This paper addresses a version of the linear quadratic control problem for mean-field stochastic differential equations with deterministic coefficients on time scales, which includes the discrete time and continuous time as special cases. Two coupled Riccati equations on time scales are given and the optimal control can be expressed as a linear state feedback. Furthermore, we give a numerical example.
Highlights
Yingjun Zhu and Guangyan JiaIs paper addresses a version of the linear quadratic control problem for mean-field stochastic differential equations with deterministic coefficients on time scales, which includes the discrete time and continuous time as special cases
Time scales were first introduced by Hilger [5] in 1988 in order to unite differential and difference equations into a general framework
Introduction e linear quadratic control problem is one of the most important issues for optimal control problem. e study of the mean-field linear quadratic optimal control problem has received much attention [1, 2], and it has a wide range of applications in engineering and finance [3, 4]
Summary
Is paper addresses a version of the linear quadratic control problem for mean-field stochastic differential equations with deterministic coefficients on time scales, which includes the discrete time and continuous time as special cases. E study of the mean-field linear quadratic optimal control problem has received much attention [1, 2], and it has a wide range of applications in engineering and finance [3, 4]. The mean-field linear quadratic control problem is studied in the version of time scales. We are interested in the mean-field stochastic linear quadratic control problem on time scales (MF-SΔLQ for short). Let f: T ⟶ R be a function and t ∈ Tκ, and if for all ε > 0, there exist a neighborhood U of t such that
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