不确定离散切换饱和系统的保成本控制  

Guaranteed Cost Control for Uncertain Discrete-time Switched Saturated Systems

作　　者：张新权[1] 赵志广[2] 柳强[1] 

机构地区：[1]辽宁石油化工大学信息与控制工程学院,辽宁抚顺113001 [2]首钢股份公司迁安钢铁公司,河北迁安064400

出　　处：《控制工程》2015年第6期1157-1160,共4页Control Engineering of China

基　　金：国家自然科学基金青年科学基金(51305192);辽宁省教育厅科研项目(L2014159)

摘　　要：基于线性矩阵不等式和保成本控制理论,研究了一类具有执行器饱和的不确定离散切换线性系统在任意切换下的保成本控制及优化设计问题。系统矩阵和输入矩阵中含有时变不确定性。目的是设计状态反馈控制律使得闭环系统渐近稳定的同时,使得所给定的成本函数的上界最小。首先,利用共同李雅普诺夫函数方法,获得了状态反馈保成本控制器存在的充分条件。进一步,为获得使得成本函数上界最小的优化设计方案,将确定成本函数最小上界的问题转化为带有线性矩阵不等式约束的凸优化问题。这种检验方法容易计算,适合在工程中使用。最后,最后通过一个数值例子验证了所提出方法的有效性。The problem of guaranteed cost control and optimization design is investigated for a class of uncertain discrete-time switched systems＇ subject to actuator saturation under arbitrary switching laws based on LMIs. Time-varying uncertainties are contained in both state matrix and input matrix. The purpose is to design a state feedback control law such that the closed-loop system is asymptotically stable and the upper-bound of the cost function is minimized. Firstly, based on the common Lyapunov function approach, some sufficient conditions for the existence of guaranteed cost controllers are obtained. Furthermore, to obtain the optimization scheme, a convex optimization problem with linear matrix inequalities （LMI） constraints is formulated to determine the minimum upper-bound of the cost function. This method is easy to check and is suitable for the engineering application. Finally, a numerical example is given to show the effectiveness of the proposed design method.

关 键 词：保成本 饱和 切换系统 共同LYAPUNOV函数 

分 类 号：TP27[自动化与计算机技术—检测技术与自动化装置]