Adaptive output-feedback tracking of stochastic nonlinear systems

We address the adaptive stabilization and tracking problems for a class of output feedback canonical systems driven by Wiener noises of unknown covariance. Filtered transformation and backstepping techniques are employed in the stochastic control design. We obtain two adaptive controllers that guarantee the global stability in probability for vanishing perturbations or the input-to-state stability in probability for nonvanishing perturbations respectively. The tracking error can converge to a small residual set around the origin in the sense of mean quartic value.