一类离散时间广义系统的迭代学习控制  

Iterative learning control of a class of discrete-time singular system

作　　者：曹伟[1] 郭媛[1] 孙明[1] 

机构地区：[1]齐齐哈尔大学计算机与控制工程学院,齐齐哈尔161006

出　　处：《物理学报》2016年第12期23-29,共7页Acta Physica Sinica

基　　金：国家自然科学基金青年科学基金(批准号:61100103);齐齐哈尔大学青年教师科研启动基金重点项目(批准号:2014k-Z15)资助的课题~~

摘　　要：针对一类离散时间广义系统,提出了一种离散迭代学习控制算法.首先,通过非奇异变换将离散时间广义系统分解为正常离散状态方程和代数方程的形式.然后,利用上一次迭代学习获得的前一时刻误差和当前时刻误差来修正上一次的控制量,从而获得下一次迭代学习的新控制量,并对算法的收敛性进行了理论证明,给出了算法收敛的充分条件.研究结果表明,所提算法能够在有限时间区间内实现系统状态对期望状态的完全跟踪.最后,通过仿真算例进一步验证了所提算法的有效性.Singular systems axe also called descriptor systems. Compared with normal systems, singular systems have become one of effective tools which can describe and characterize varieties of real systems, because they can better describe physical properties of the systems. Up to now, the analyses and syntheses of singular systems have been widespread applied to linear matrix inequality （LMI） method. The method requires known systems to have accurate mathematical model information, however, real systems have difficulties in obtaining their accurate mathematical models, owing to the fact that real systems are frequently subjected to all kinds of interferences, uncertainties, and nonlinear factors. Specially, in the case of singular systems, obtained LMI conditions often have a constraint equation or LMI is semi-definite, which makes it more difficult to solve LMI. Therefore, in order to avoid the above two problems occurring in settling state tracking issue for singular systems, in the meantime, for convenience of computating control algorithm and information storage, in this paper we propose a discrete-time iterative learning control algorithm for a class of discrete-time singular system with repetitive running characteristics in finite time interval. The specific process is divided into two steps. First, the class of discrete-time singular system is decomposed into normal discrete-time state equation and algebraic equation form by nonsingular transformation. Accordingly, the singular system state is also decomposed into two parts. Among them, the dimension of the first part state is equal to singular matrix rank and another is equal to system dimension minus singular matrix rank. In addition, the control law of last iterative learning is modified by using two tracking errors at two different times： one error is real-time tracking error generated from the comparison between the first part state and its desired state and another is tracking error at a previous time generated from comparison between the second part s

关 键 词：广义系统 迭代学习控制 非奇异变换 状态跟踪 

分 类 号：O231[理学—运筹学与控制论]