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1. Introduction
Sliding mode variable structure control theory is essentially a kind of special nonlinear control, and its nonlinear performance is the discontinuity for the control [1]. Due to the rapid development of computer technology, discrete-time system is widely used in the actual control; therefore, the sliding mode control for discrete-time system is especially important [1, 2]. Based on the reaching law, Gao et al. proposed the discrete sliding mode variable structure control [3]. Koshkouei and Zinober proposed the existence conditions of a new sliding mode and designed a new sliding mode control law [4]. But it is difficult to effectively guarantee the robustness of sliding mode control. Chen studied sliding mode control for the multiple input-output discrete-time system with disturbances and unknown parameters, and an adaptive law was implemented to estimate the unknown term [5].
Artificial neural network has strong learning ability and high ability of parallel computing, and it can approximate any nonlinear function and has good robustness and fault tolerance [6, 7]. In recent years, the combination of neural network with sliding mode variable structure control method [8–10] has become a new field for variable structure development. The nonlinear part of neural network, uncertainties, and unknown external disturbance were estimated online for the linear system, and the equivalent control was realized based on the neural network, and the chattering was eliminated effectively [11]. Ertugrul and Kaynak proposed a new sliding mode control method based on neural network, which used two neural networks to approximate equivalent sliding mode control and the part of switching sliding mode control, without object model, and it effectively eliminated the chattering [12]. Huang et al. designed a sliding mode controller by using the approximation ability of RBF neural network; the switching function was regarded as the input of the network, the controller was completely realized by continuous RBF function, and this method cancelled the switching part...