Stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function

A more general class of stochastic non-linear systems with unmodelled dynamics and uncertain non-linear functions are considered in this paper. With the concept of ISpS being extended to stochastic case, by combining changing supply function technique with backstepping design technique, an adaptive output-feedback controller is proposed. It is shown that all the solutions of the closed-loop system are uniformly bounded in probability, and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability. A simulation example demonstrates the control scheme.