Stochastic Simultaneous Stabilization and Parking Control of the Brockett Integrator

Abstract

This paper proposes a design of stochastic control laws for simultaneous stabilization and parking (i.e., tracking a reference trajectory that converges to the desired configuration) of the Brockett integrator based on Lyapunov's direct method, recent developments in the stabilization of stochastic systems, and Itô's formula for nonsmooth (weakly differentiable) functions. The control laws use two independent Wiener processes with the same covariance and the reference trajectory update. The proposed control design guarantees global K∞-exponential stability of the closed-loop system in probability.