New Approach to General Nonlinear Discrete-Time Stochastic $H_\infty$ Control

TL;DR

This paper introduces a convex analysis-based method for solving the $H_$ control problem in discrete-time nonlinear stochastic systems, including a stochastic bounded real lemma and state feedback control design.

Contribution

It presents a novel convex analysis approach and a stochastic bounded real lemma for $H_$ control, advancing nonlinear stochastic control theory.

Findings

Effective control design demonstrated through two examples.

New stochastic bounded real lemma established.

Convex analysis approach proved successful for nonlinear stochastic systems.

Abstract

In this paper, a new approach based on convex analysis is introduced to solve the $H_\infty$ problem for discrete-time nonlinear stochastic systems. A stochastic version of bounded real lemma is proved and the state feedback $H_\infty$ control is studied. Two examples are presented to show the effectiveness of our developed theory.