基于矩阵半张量积方法的带有敌对输入的异步时序机控制  

Control of asynchronous sequential machine with adversarial input based on the semi-tensor product of matrices

作　　者：陈增强 王晶晶[1,2] 韩晓光 张青[3] Zengqiang CHEN;Jingjing WANG;Xiaoguang HAN;Qing ZHANG(College of Computer and Control Engineering,Nankai University,Tianjin 300350,China;Key Laboratory of Intelligent Robotics of Tianjin,Nankai University,Tianjin 300350,China;College of Science,Civil Aviation University of China,Tianjin 300300,China)

机构地区：[1]南开大学计算机与控制工程学院,天津300350 [2]南开大学天津市智能机器人技术重点实验室,天津300350 [3]中国民航大学理学院,天津300300

出　　处：《中国科学：信息科学》2019年第11期1488-1501,共14页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:61573199);天津市自然科学基金(批准号:14JCYBJC18700)资助项目

摘　　要：本文基于矩阵半张量积方法研究了带有敌对输入的异步时序机的控制问题.首先,利用矩阵半张量积,给出了带有敌对输入的异步时序机动态行为的代数表示.接着,通过分析具体的控制过程设计了具有最小状态集的控制器并给出了控制器状态转移结构矩阵和输出结构矩阵的赋值算法.其次,基于带有敌对输入的异步时序机的代数表示和控制器的赋值算法给出了整个闭环系统的动态行为的代数表示,从而验证本文理论结果的正确性.最后,利用具体实例说明了本文所提方法的的可行性和有效性.In this study, we investigate the control problem of asynchronous sequential machine with adversarial input by using the semi-tensor product(STP) of matrices. First, by applying the STP of matrices, a new algebraic expression of asynchronous sequential machines with an adversarial input is deduced. Next, by investigating the control process, the controller with the minimal state set is designed, and two algorithms for assigning the values to the state transition structure matrix and the output structure matrix of the controller are proposed. Then,in the framework of the algebraic expression of the asynchronous sequential machines with adversarial input and two proposed algorithms, an algebra expression of the closed-loop system dynamic is established;the theoretical results are verified by using this algebra expression. Finally, an example is presented to illustrate the validity and application of the proposed approach.

关 键 词：敌对输入 异步时序机 矩阵半张量积 控制器 转移结构矩阵 输出结构矩阵 

分 类 号：O15[理学—数学]