I. Introduction
In the past decades, adaptive fuzzy/neural network control for the deterministic nonlinear systems has been extensively studied based on the backstepping technique proposed first in [1], and many significant results were obtained (see [2]–[6] and the references therein). The nonlinear stochastic systems model and control were also paid much attention due to their extensive applications in economic, social, and industry systems [7]–[11], where [9] and [10] proposed the adaptive control approaches based on the event-triggering mechanism. It is noted that the above nonlinear systems are in strict-feedback (or pure-feedback) forms. The nonstrict-feedback nonlinear systems considered in [12] are more general than the strict-feedback ones. The above control strategies may be no longer effective since the higher-order variables will appear in the low-order subsystems, which can give rise to the problem of the algebraic loop by the backstepping technique. To overcome this problem, a monotone bounded increasing function was introduced into the adaptive controller design in [13] and [14]. The approach was further extended to the nonlinear stochastic systems with backlash-like hysteresis in [15]. It should be noted that these kinds of monotonic bound increasing functions may greatly limit the practical application. How to develop a new approach to overcome that limitation is one of the motivations of this article.