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 Neural-Network-Based Adaptive Backstepping Control With Application to Spacecraft Attitude Regulation Xibin Cao, Peng Shi, Fellow, IEEE , Zhuoshi Li, and Ming Liu Abstract— This paper investigates the neural-network-based adaptive control problem for a class of continuous-time nonlinear systems with actuator faults and external disturbances. The model uncertainties in the system are not required to satisfy the norm-bounded assumption, and the exact information for compo- nents faults and external disturbance is totally unknown, which represents more general cases in practical systems. An indirect adaptive backstepping control strategy is proposed to cope with the stabilization problem, where the unknown nonlinearity is approximated by the adaptive neural-network scheme, and the loss of effectiveness of actuators faults and the norm bounds of exogenous disturbances are estimated via designed online adaptive updating laws. The developed adaptive backstepping control law can ensure the asymptotic stability of the fault closed- loop system despite of unknown nonlinear function, actuator faults, and disturbances. Finally, an application example based on spacecraft attitude regulation is provided to demonstrate the effectiveness and the potential of the developed new neural adaptive control approach. Index Terms— Actuator degradation, adaptive control, back- stepping control, neural network, spacecraft attitude regulation. I. I NTRODUCTION I T IS known that neural network possesses powerful approximation capability, and has become a popular tool to evaluate unknown function in control theory domain [10], [12], [21]. The corresponding neural-network- based control schemes have been further proven to be appro- priate strategies to achieve satisfactory control performance for various complicated nonlinear systems [3], [15]. In the past decades, a wealth of results concerned with adaptive neural control has been reported in the existing literature [16], [21]. Manuscript received August 4, 2016; revised February 26, 2017 and August 31, 2017; accepted September 6, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 91438202, Grant 61473096, Grant 61690212, Grant 61333003, and Grant U1509217, in part by the Australian Research Council under Grant DP170102644, in part by the New Century Excellent Talents Program of the Ministry of Education of the People’s Republic of China under Grant NCET-13-0170, and in part by the 111 Project under Grant B17048. (Corresponding author: Ming Liu.) X. Cao, M. Liu, and Z. Li are with the School of Astronautics, Harbin Institute of Technology, Harbin 150001, China (e-mail: mingliu23@163.com). P. Shi is with the School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, SA 5005, Australia, and also with the Col- lege of Engineering and Science, Victoria University, Melbourne, VIC 8001, Australia (e-mail: peng.shi@adelaide.edu.au). 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.2017.2756993 Among these interesting works, adaptive backstepping control via neural-networks approximation has attracted considerable research attention [17], [23], [28]. To mentioned a few, adap- tive backstepping neural-network control with state feedback case has been developed for uncertain multi-input multioutput nonlinear systems in [2] and [9]. Output feedback or observer- based adaptive neural-network control problems have been investigated for stochastic nonlinear systems in [30] and [31]. On the other hand, in practical applications, the failure of control components (sensors, actuators, and the plant itself) always exists with unknown size of faults, which may result in performance degradation or even instabili- ties [8], [27]. Hence, fault-tolerant control design problems have recently attracted persistent attention, and a variety of control approaches have been developed for various systems, such as linear systems [26], nonlinear systems [16], [29], time- delay systems [3], [6], and stochastic systems [13], [14], [24]. The fault-tolerant control strategies in the existing literature can be divided into two types, i.e., the passive approach and the active approach [11]. In the passive method, a fixed- gain control law is synthesized to maintain the stability and performance of systems not only when all control components are operational, but also when some admissible components failures occur [25]. However, the main limitation of the passive method is that the designed static gain controller may be conservative to cope with possible multiple-mode faults [1]. In contrast, the main idea of active approaches is to compensate for sensor/actuator faults either by implementing a predesigned controller or by constructing a new control law online [19]. In this research forefront, a lot of active approaches have been proposed, such as fault detection-based methods [4] and sliding mode observer-based designs [7], [20]. It should be pointed out that, in the aforementioned lit- erature, the knowledge of norm bounds of faults and exter- nal disturbance is always supposed to be available, which are, however, difficult to be measured in practice due to physical constraints. In addition, in these existing works, the model nonlinearities are mostly supposed to meet the so-called norm-bounded condition. These two assumptions may lead to constrained applicability of those presented control schemes in practice. Therefore, how to reduce the conservativeness on requirement of norm bounds of faults and model nonlinear function, has become a challenging and significant research topic. Such a problem has not yet received 2162-237X © 2017 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.