In this paper, the sliding mode preview control problem for a class of continuous-time linear systems is studied. Firstly, an extended error system consisting of the error equation and the state equation of the original system is constructed, and the tracking problem is transformed into the regulation problem. Secondly, a quadratic performance index function is introduced for the state variables of the extended error system, and the preview sliding surface is designed based on the existing conclusions of the optimal preview control. Thirdly, the sliding mode controller with preview effect for the extended error system is designed by using the reaching law method; then, the desired sliding mode preview controller of the original system can be obtained through the integral. The numerical simulation verifies the feasibility of the proposed method.

中文翻译：

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一类连续时间线性系统的滑模预览控制

本文研究了一类连续时间线性系统的滑模预览控制问题。首先构造由误差方程和原系统状态方程组成的扩展误差系统，将跟踪问题转化为调节问题。其次，针对扩展误差系统的状态变量引入了二次性能指标函数，并根据已有的最优预控控制结论设计了预控滑动面。第三，利用到达律方法设计了具有扩展误差系统预览效果的滑模控制器；然后，通过积分可以得到原系统所需的滑模预览控制器。数值模拟验证了所提出方法的可行性。