Maximum principle for discrete-time control systems driven by fractional noises and related backward stochastic difference equations

TL;DR

This paper develops a stochastic maximum principle for discrete-time control systems influenced by fractional noises, using backward stochastic difference equations, and applies it to linear quadratic problems.

Contribution

It introduces a novel maximum principle for systems driven by fractional noises using backward stochastic difference equations, expanding control theory in stochastic systems.

Findings

Established a maximum principle for fractional noise-driven systems

Analyzed solutions of backward stochastic difference equations with fractional noises

Applied results to linear quadratic control problems

Abstract

In this paper, the optimal control for discrete-time systems driven by fractional noises is studied. A stochastic maximum principle is obtained by introducing a backward stochastic difference equation contains both fractional noises and the constructed white noises. The solution of the backward stochastic difference equations is also investigated. As an application, the linear quadratic case is considered to illustrate the main results.