Stochastic Linear Quadratic Control Problem on Time Scales

Abstract

This paper addresses a version of the stochastic linear quadratic control problem on time scales S Δ LQ , which includes the discrete time and continuous time as special cases. Riccati equations on time scales are given, and the optimal control can be expressed as a linear state feedback. Furthermore, we present the uniqueness and existence of the solution to the Riccati equation on time scales. Furthermore, we give an example to illustrate the theoretical results.

Linear Feedback of Mean-Field Stochastic Linear Quadratic Optimal Control Problems on Time Scales

“…□ Remark 6. When A, B, D, Q, R, and G are all equal to zero, then P � 􏽢 P. is recovers the result of the classical SΔLQ problem [24].…”

“…Substituting it into (47), we have the optimal cost functional can be expressed as (38). For the existence and uniqueness of the solutions to the RΔEs, it is assert [24] that Riccati equation (33) admits as a unique positive semidefinite solution P since (H2) holds. It follows that 􏽢 K > 0.…”

“…At the same time, some results were obtained for the linear quadratic control problems for deterministic linear system on time scales in [22,23]. In [24], the authors developed the linear quadratic control problems for stochastic linear system on time scales. To our best knowledge, the optimal control problems for the mean-field system on time scales have not been established.…”