Stochastic Linear Quadratic Control Problem on Time Scales

Abstract

This paper addresses a version of the stochastic linear quadratic control problem on time scales $\left(\text{S}\mathrm{\Delta }\text{LQ}\right)$ , 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.