不确定周期离散时间系统的预见饱和控制  

Preview Saturated Control for Uncertain Periodic Discrete-Time Systems

作　　者：李丽[1,2] 卢延荣 宋沈忆 LI Li;LU Yanrong;SONG Shenyi(School of Statistics and Mathematics,Hubei University of Economics,Wuhan 430205;Hubei Center for Data and Analysis,Hubei University of Economics,Wuhan 430205;College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 730050)

机构地区：[1]湖北经济学院统计与数学学院,武汉430205 [2]湖北经济学院湖北数据与分析中心,武汉430205 [3]兰州理工大学电气工程与信息工程学院,兰州730050

出　　处：《系统科学与数学》2024年第1期99-114,共16页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61903130);湖北省自然科技基金(2022CFB139)资助课题.

摘　　要：文章考虑一类具有输入饱和的不确定周期离散时间系统的预见饱和控制问题.由于时变不确定矩阵及输入饱和的存在,预见控制理论中经典的差分算子方法无法适用.为此,文章引入状态辅助变量,利用系统状态向量与状态辅助变量之差代替通常的状态差分,成功地构造出输入饱和不确定离散系统的扩大误差系统.通过扩大误差系统的构造,将原系统的预见饱和控制器的设计问题转化为扩大误差系统的镇定问题.利用改进的扇形条件处理饱和非线性项并结合线性矩阵不等式(LMI)技巧,导出了闭环系统渐近稳定的充分条件.最后,仿真例子表明了文章结果的有效性.This paper considers the problem of preview saturated control for uncertain periodic discrete-time systems with actuator saturation.The classical difference operator method in preview control theory can not be applied due to the existence of time-varying uncertain matrix and input saturation.The state auxiliary variable is introduced and the usual state difference is replaced by the the difference between the state vector and the state auxiliary variable.Therefore,the augmented error system of uncertain discrete system with input saturation is successfully constructed.By constructing the augmented model,the problem of designing the preview saturation controller of the original system is transformed into the problem of stabilization of the augmented error system.A sufficient condition for the asymptotic stability of the closed-loop system is derived by using the improved sector condition to deal with the saturation nonlinearity and the LMI technique.Finally,a simulation example is given to illustrate the validity of the results.

关 键 词：扩大误差系统 预见控制 不确定周期系统 输入饱和 状态反馈 输出反馈 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]