In this article, the observer-based preview tracking control problem is investigated for a class of discrete-time Lipschitz nonlinear systems. To convert the observer-based trajectory tracking problem into a regulation problem, the classical difference technique is used to construct an augmented error system containing tracking error signal and previewable reference knowledge. Then, a state feedback controller with specific structures is taken into consideration. Sufficient design condition is established, based on the Lyapunov function approach, to guarantee the asymptotic stability of the closed-loop system. By means of some special mathematical derivations, the bilinear matrix inequality condition is successfully transformed into a tractable linear matrix inequality. Meanwhile, the gains of both observer and tracking controller can be computed simultaneously only in one step. As for the original system, the developed tracking control law is composed of an integrator, an observer-based state feedback controller, and a preview action term related to the reference signal. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical method.

在本文中，针对一类离散时间Lipschitz非线性系统，研究了基于观察者的预览跟踪控制问题。为了将基于观察者的轨迹跟踪问题转换为调节问题，经典差分技术用于构建包含跟踪误差信号和可预览参考知识的增强误差系统。然后，考虑具有特定结构的状态反馈控制器。基于李雅普诺夫函数法，建立了充分的设计条件，以保证闭环系统的渐近稳定性。通过一些特殊的数学推导，双线性矩阵不等式条件成功地转化为可处理的线性矩阵不等式。与此同时，观察者和跟踪控制器的增益只能在一个步骤中同时计算。对于原始系统，开发的跟踪控制律由积分器，基于观察者的状态反馈控制器和与参考信号相关的预览动作项组成。最后，提供了两个数值示例来证明该理论方法的有效性。