This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 1 Observer-Based Adaptive Neural Network Control for Nonlinear Systems in Nonstrict-Feedback Form Bing Chen, Huaguang Zhang, Senior Member, IEEE , and Chong Lin, Senior Member, IEEE Abstract—This paper focuses on the problem of adaptive neural network (NN) control for a class of nonlinear nonstrict- feedback systems via output feedback. A novel adaptive NN backstepping output-feedback control approach is first pro- posed for nonlinear nonstrict-feedback systems. The monotonicity of system bounding functions and the structure character of radial basis function (RBF) NNs are used to overcome the difficul- ties that arise from nonstrict-feedback structure. A state observer is constructed to estimate the immeasurable state variables. By combining adaptive backstepping technique with approxima- tion capability of radial basis function NNs, an output-feedback adaptive NN controller is designed through backstepping approach. It is shown that the proposed controller guarantees semiglobal boundedness of all the signals in the closed-loop systems. Two examples are used to illustrate the effectiveness of the proposed approach. Index Terms— Adaptive neural control, backstepping, nonlinear systems, nonstrict-feedback structure. I. I NTRODUCTION I N THE past decade, there has been an increasing interest in approximation-based adaptive control for nonlinear systems. With the inherent approximation capability of neural networks (NNs) or fuzzy logic systems, some adaptive neural/fuzzy controllers were proposed for nonlinear systems [1]–[14]. In [1]–[11], the problem of stabilization or tracking control was addressed for single-input and single-output (SISO) nonlinear strict- feedback systems, and the corresponding adaptive neural/fuzzy controllers were developed via state feedback control strategy. Furthermore, adaptive neural/fuzzy control was discussed for multi-input and multioutput (MIMO) nonlinear strict-feedback systems in [12]–[14], respectively. Notice that state variables are usually unknown or partly known in practice, and thus the aforementioned control strategies via state feedback are difficult to be implemented. Therefore, some output-feedback control strategies were developed in recent years. Adaptive NN output-feedback Manuscript received August 13, 2014; revised December 25, 2014 and March 1, 2015; accepted March 6, 2015. This work was supported by the National Natural Science Foundation of China under Grant 61473160, Grant 61174033, and Grant 61034005. B. Chen and C. Lin are with the Institute of Complexity Science, Qingdao University, Qingdao 266071, China (e-mail: chenbing1958@ 126.com; linchong2004@hotmail.com). H. Zhang is with the School of Information Science and Engineering, Northeastern University, Shenyang 110006, China (e-mail: zhanghuaguang@mail.neu.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNNLS.2015.2412121 control was addressed in [15]–[19]. Leu et al. [15] addressed observer-based adaptive fuzzy-neural control for a class of SISO nonlinear systems, and an indirect adaptive fuzzy- neural controller was proposed. An observer-based direct adaptive fuzzy-neural controller was developed in [16]. In [17], the problem of adaptive NN output-feedback control was investigated for two classes of nonlinear discrete-time systems with unknown control directions, and an unified approach of control design was proposed. Tong et al. [18] addressed adaptive NN backstepping control for a class of delayed large-scale systems, and decentralized adaptive NN output-feedback controllers were developed. It was provided that under the action of suggested neural controllers, the adaptive closed-loop systems were semiglobally uniformly ultimately bounded (SGUUB). In [19], adaptive output-feedback neural control was first considered for stochastic nonlinear delayed systems with strict-feedback structure. The proposed control scheme employed only one NN to compensate for all unknown nonlinear terms. In those works, unknown nonlinear terms in systems were assumed to be the functions of system’s outputs only. In [20]–[22], observer-based output-feedback adaptive fuzzy backstepping control scheme was proposed for SISO nonlinear strict-feedback systems. The corresponding work was considered for discrete-time nonlinear systems in [23]. The constructed adaptive fuzzy controller guaranteed that the closed-loop systems were uniformly ultimately bounded. The work was further extended from SISO systems to MIMO systems in [24] and [25], where the effect from unknown dead zone on controlled systems was considered. In [26], an input-driven filter was first introduced to estimate the immeasurable state variables; furthermore, an adaptive output-feedback fuzzy tracking controller was proposed for nonlinear systems in lower triangle form. This work was further extended to nonlinear stochastic strict-feedback systems in [27]. In [28], using NNs to approximate unknown nonlinear functions, an output-feedback adaptive neural controller was presented for nonlinear strict-feedback systems with time delays. In [29], adaptive output-feedback fuzzy control was discussed. An output-feedback fuzzy controller was developed for nonlinear delayed strict-feedback systems with unknown control direction. Although adaptive NN/fuzzy backstepping control has been one of the most popular design approaches to a class of nonlinear systems, the existing adaptive backstepping approaches suffer from a major limitation of 2162-237X © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.