Stochastic Asymptotic Stabilizers for Deterministic Input-Affine Systems based on Stochastic Control Lyapunov Functions

TL;DR

This paper introduces a stochastic stabilization approach for deterministic control systems using stochastic control Lyapunov functions, enabling global asymptotic stability in probability through a new feedback law.

Contribution

It develops a sufficient condition for diffusion coefficients to ensure the existence of stochastic control Lyapunov functions for input-affine systems.

Findings

Established a sufficient condition for diffusion coefficients.

Designed a stochastic feedback law for Brockett integrator.

Achieved global asymptotic stability in probability.

Abstract

In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the diffucion coefficients so that there exist stochastic control Lyapunov functions for the systems. To illustrate the usefulness of the sufficient condition, the authors propose the stochastic continuous feedback law, which makes the origin of the Brockett integrator become globally asymptotically stable in probability.