Regulation of partially known nonlinear stochastic systems using fast identification

We investigate the stability of an exact linearization style of control algorithm applied to a class of partially known nonlinear stochastic systems sampled at a constant rate. Since the system dynamics are not known, they are estimated using a filter which places very few assumptions on the underlying structure of the system. We show that when certain mild smoothness conditions are satisfied and the sampling rate is sufficiently fast, the control algorithm stabilizes the system in the sense that the closed-loop system becomes an ergodic Markov chain. Moreover, an explicit bound for the expected deviation of the system state from the origin is given