I. Introduction
Lower triangular nonlinear systems are a special class of nonlinear systems, which can be used to describe a large number of practical systems such as Brusselator model, one-link robot system, ball, and beam system, etc., and the research of such systems has drawn intensive attention in recent years. Some excellent control schemes [1]–[9] have been reported. In particular, adaptive fuzzy/neural control is one of the effective control schemes, which has been widely studied since fuzzy logic system (FLS) and neural network have a good theoretical property in approximating the unknown nonlinear function (see [10]–[13] and the references therein). However, the control schemes mentioned above cannot be directly applied to nonlower triangular nonlinear systems such as pure-feedback system and nonstrict-feedback system [14]–[19] . For nonstrict-feedback system, the nonlinear function existed in the th subsystem involves full state variables , which may result in algebraic loop problem if those methods of lower triangular system [2], [4], [20] are adopted directly. To tackle such a difficulty, much work has been reported. To list a few, in [21], the authors developed a suite of adaptive optimal control for a kind of nonlinear discrete-time system expressed in nonstrict-feedback form. In [22], based on backstepping technique, Chen et al. developed an effective approach called variable separation to overcome the difficulty resulted from the nonstrict-feedback structure. However, the result in [22] requires that the nonlinear functions are monotonically increasing. To relax such a restriction on nonlinear functions , Tong et al. in [23] proposed a new control scheme utilizing the property of fuzzy basis functions, which makes the controller design process simpler.