Information Sciences 426 (2018) 50–60 Contents lists available at ScienceDirect Information Sciences journal homepage: www.elsevier.com/locate/ins Neural networks-based command filtering control of nonlinear systems with uncertain disturbance Jinpeng Yu ∗ , Bing Chen, Haisheng Yu, Chong Lin, Lin Zhao The College of Automation and Electrical Engineering, Qingdao University, Qingdao 266071 PR China a r t i c l e i n f o Article history: Received 13 October 2016 Revised 25 September 2017 Accepted 11 October 2017 Available online 13 October 2017 Keywords: Nonlinear systems Neural networks-based adaptive control Backstepping a b s t r a c t This paper is concerned with neural networks-approximation based command filtering backstepping control for uncertain strict-feedback nonlinear systems with unknown distur- bances. The “explosion of complexity” problem arising from the virtual controllers’ deriva- tives is resolved by utilizing the command filtering technique, and the shortcoming exist- ing in dynamic surface method is properly overcome via an introduced error compensation mechanism (ECM). Moreover, the nonlinear functions of the underlying system are well ap- proximated by exploiting neural networks-based framework. The developed strategy may cover two features with comparison of current achievements: 1) The filtering error can be eliminated in the light of the designed compensating signals; 2) The requirement of adap- tive parameters is reduced to only one, which may enhance the control performance for realistic project implementation. At last, an application example in position tracking con- trol of surface permanent magnet synchronous motor (SPMSM) is carried out to further verify the effectiveness and advantages of the theoretical result. © 2017 Published by Elsevier Inc. 1. Introduction As is well-known, in view of the excellent ability of asymptotic tracking and global stability for strict-feedback nonlinear systems [11], adaptive backstepping control method has been widely applied to controller design in nonlinear systems [15,16,22]. Nevertheless, it is commonly recognised that there may be two problems restricting wide utilization of the clas- sical backstepping: one is that “certain functions may not be nonlinear” [5,34,35], another is the “explosion of complexity” (EOC) issue [2,6,14,26,29,38,40,42]. On the other hand, with the increasing emergence of approximation theory, e.g., fuzzy logic system (FLS) [1,3,4,10,21,23–25,27,28,30,31,45] or neural networks (NNs) [12,13,33,39,41,43,46,47,50] approximators, adaptive control methods have been updated constantly for the analysis and synthesis of uncertain nonlinear systems. It should be mentioned that, the first issue existing in the adaptive backstepping has been successfully tackled by the adaptive fuzzy or NNs control strategy, which may be regarded as one of the systematic methodologies for the approximation of nonlinear functions. Then, the second one, i.e., EOC, may not be fully settled via the aforementioned control approach [36]. In recent years, it is noted that dynamic surface control (DSC) [18,32,44] has been put forward to solve the EOC problem [19,20,37]. But the issue of errors arising from the filter is not concerned by the NNs controllers and the DSC approach, which may affect the system performance to some degree. In this way, the command filtered backstepping method was proposed for the EOC in [8], after which a command filter-based backstepping was properly generalized to the adaptive case ∗ Corresponding author. E-mail address: yjp1109@hotmail.com (J. Yu). https://doi.org/10.1016/j.ins.2017.10.027 0020-0255/© 2017 Published by Elsevier Inc.