Control design for partial stabilization of nonlinear mechanical systems with random disturbances

TL;DR

This paper introduces a control design method for nonlinear stochastic mechanical systems that achieves partial stabilization in probability, demonstrated through mechanical examples.

Contribution

A new constructive control approach for partial stabilization of nonlinear stochastic systems, ensuring asymptotic stability in probability for selected state variables.

Findings

Control method achieves partial stabilization in probability.

Mechanical examples validate controller effectiveness.

Method applicable to nonlinear stochastic systems.

Abstract

The problem of partial stabilization for nonlinear control systems described by the Ito stochastic differential equations is considered. For these systems, we propose a constructive control design method which leads to establishing the asymptotic stability in probability of the trivial solution of the closed-loop system with respect to a part of state variables. Mechanical examples are presented to illustrate the efficiency of the obtained controllers.