Stochastic Linear Quadratic Control Problem on Time Scales

Abstract

This paper addresses a version of the stochastic linear quadratic control problem on time scales SΔLQ, 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.