IEEE Trans Cybern. 2015 Mar;45(3):497-505. doi: 10.1109/TCYB.2014.2329495.
In the paper, an adaptive tracking control design is studied for a class of nonlinear discrete-time systems with dead-zone input. The considered systems are of the nonaffine pure-feedback form and the dead-zone input appears nonlinearly in the systems. The contributions of the paper are that: 1) it is for the first time to investigate the control problem for this class of discrete-time systems with dead-zone; 2) there are major difficulties for stabilizing such systems and in order to overcome the difficulties, the systems are transformed into an n-step-ahead predictor but nonaffine function is still existent; and 3) an adaptive compensative term is constructed to compensate for the parameters of the dead-zone. The neural networks are used to approximate the unknown functions in the transformed systems. Based on the Lyapunov theory, it is proven that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of zero. Two simulation examples are provided to verify the effectiveness of the control approach in the paper.
本文针对一类具有死区输入的非线性离散时间系统，研究了自适应跟踪控制设计问题。所考虑的系统为非仿射纯反馈形式，死区输入在系统中呈非线性。本文的贡献在于：1）首次研究了这一类具有死区的离散时间系统的控制问题；2）稳定此类系统存在主要困难，为了克服这些困难，将系统转换为 n 步超前预测器，但仍然存在非仿射函数；3）构造了一个自适应补偿项来补偿死区的参数。在转换后的系统中使用神经网络来逼近未知函数。基于李雅普诺夫理论，证明了闭环系统中的所有信号都是半全局一致最终有界的，跟踪误差收敛到零的一个小邻域内。提供了两个仿真示例来验证本文控制方法的有效性。
