I. Introduction
In recent years, there has been a significant growth of researches on uncertain nonlinear systems. In practical processes, there always exist model errors, outside interferences and measurement noises, which can affect the control performance, and these disturbances can be viewed as unmodeled dynamics. In [1], Jiang and Praly designed a dynamic signal used to represent unmodeled dynamics, and the states were globally uniformly ultimately bounded (UUB) via a control method. Subsequently, Jiang [2] presented an output feedback control method by combining small-gain theorem with partial-state observer. Afterwards, RBFNN or fuzzy logic systems (FLSs) were combined with the designed dynamic signal or small gain theorem in various researches, and two representative adaptive backstepping control laws were developed in [3] and [4]. Considering the problem that the effect of standard adaptive controllers is not ideal for the large system uncertainties, Dogan et al. [5] designed a controller that can relax the stability limit. For a lower triangular stochastic systems with unmodeled states, Xia et al. [6] applied an output feedback control law by combining a dynamic signal with stochastic stability. So far, there are many significant control laws proposed for the systems with unmodeled states, such as [7]–[12]. These control schemes are implemented in the field of systems with known control directions, however, the control directions sometimes are unknown in practice [13].