Further results on output-feedback regulation of stochastic nonlinear systems with SiISS inverse dynamics

This article further discusses the problem of output-feedback regulation for more general stochastic nonlinear systems with stochastic integral input-to-state stable inverse dynamics, and focuses on solving the important and unsolved problem proposed in Yu and Xie (Yu, X., and Xie, X.J. (2010), 'Output Feedback Regulation of Stochastic Nonlinear Systems with Stochastic iISS Inverse Dynamics', IEEE Transactions on Automatic Control, 55, 304-320): How to weaken the conditions on nonlinearities in drift and diffusion vector fields? Under the weaker conditions, how to make full use of the known information of stochastic nonlinear systems to design an adaptive output-feedback controller such that all the closed-loop signals are almost surely bounded and the output is driven to zero almost surely?.