Adaptive output-feedback control for stochastic nonlinear systems with zero dynamics

A class of stochastic nonlinear systems with unknown bounded parameters and zero dynamics are considered in this paper. By a series of coordinate changes, the original system is re-parameterized, which is suit for using the reduced-order observer and 1-dimension adaptive law to reduce the dynamic order of closed-loop system. In adaptive backstepping design, the quadratic and the quartic Lyapunov functions are presented simultaneously to reduce the static order of nonlinearities. It is shown that all the solutions of the closed-loop system are regulated to an arbitrarily small neighborhood of the origin in probability. Due to the order reduction of the controller, the design scheme in this paper has more practical values. A simulation example demonstrates the control scheme.