Mean-field type discrete stochastic linear quadratic optimal control problems

TL;DR

This paper investigates optimal control strategies for discrete-time stochastic systems influenced by mean-field effects and noise, providing a theoretical framework for quadratic cost minimization.

Contribution

It develops a novel mean-field type discrete stochastic LQ control approach with deterministic coefficients and weights, extending existing control theories.

Findings

Derivation of optimal control laws for mean-field stochastic systems

Analysis of system stability under the proposed control

Explicit solutions for the quadratic cost functional

Abstract

In this paper, we consider linear quadratic optimal control with mean-field type for discrete-time stochastic systems with state and control dependent noise. An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.