Stabilization of Brockett integrator using Sussmann-type artificial Wiener processes

In this paper, we derive stochastic asymptotic state-feedback stabilizers for Brockett integrators by using simple stochastic control Lyapunov functions and Sussmann-type artificial Wiener processes. First, we consider the problem of controlling nonholonomic systems via Brockett integrators. Second, we show properties of stochastic asymptotic stability in probability (GASIP) and exponential almost sure asymptotic stability (EASAS). Third, we summarize Sussmann´s approximation theorem to randomize Brockett integrators. Then, we design two stochastic state-feedback laws such that the origins become GASIP and EASAS, respectively. We also confirm the validity of our method via numerical simulations.