Max-Plus (A,B)-Invariant Spaces and Control of Timed Discrete-Event Systems

Ricardo David Katz

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Max-Plus (A,B)-Invariant Spaces and Control of Timed Discrete-Event Systems

机译：Max-Plus（A，B）不变空间和定时离散事件系统的控制

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The concept of (A,B)-invariant subspace (or controlled invariant) of a linear dynamical system is extended to linear systems over the max-plus semiring. Although this extension presents several difficulties, which are similar to those encountered in the same kind of extension to linear dynamical systems over rings, it appears capable of providing solutions to many control problems like in the cases of linear systems over fields or rings. Sufficient conditions are given for computing the maximal (A,B)-invariant subspace contained in a given space and the existence of linear state feedbacks is discussed. An application to the study of transportation networks which evolve according to a timetable is considered

机译：线性动力系统的（A，B）不变子空间（或受控不变）的概念已扩展到最大正半环上的线性系统。尽管此扩展存在一些困难，类似于在环上线性动力学系统的同类扩展中遇到的困难，但它似乎能够为许多控制问题提供解决方案，例如在磁场或环上线性系统的情况下。给出了计算包含在给定空间中的最大（A，B）不变子空间的充分条件，并讨论了线性状态反馈的存在。考虑根据时间表发展的交通网络研究应用

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《IEEE Transactions on Automatic Control》 |2007年第2期|p.229-241|共13页
作者
Ricardo David Katz;
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正文语种 eng
中图分类自动化系统;
关键词
discrete event systems; linear systems; state feedback; time-varying systems; traffic control; transportation; linear dynamical system; linear state feedback; max plus semiring; maximal (A, B) invariant spaces; timed discrete event system; transportation network; Di;

机译：离散事件系统;线性系统;状态反馈;时变系统;交通控制;运输;线性动力系统;线性状态反馈;最大加半环;最大（A;B）不变空间;定时离散事件系统;运输网络;Di;

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专利

1. Max-Plus $(A,B)$-Invariant Spaces and Control of Timed Discrete-Event Systems [J] . Ricardo David Katz IEEE Transactions on Automatic Control . 2007,第期

机译：Max-Plus $（A，B）$不变空间和定时离散事件系统的控制
2. Analysis and control of max-plus linear discrete-event systems: An introduction [J] . Discrete event dynamic systems: Theory and applications . 2020,第1期

机译：MAX-PLUS线性离散事件系统的分析与控制：介绍
3. DUALITY BETWEEN INVARIANT SPACES FOR MAX-PLUS LINEAR DISCRETE EVENT SYSTEMS [J] . Di Loreto M, Gaubert S, Katz RD, SIAM Journal on Control and Optimization . 2010,第7a8期

机译：MAX-PLUS线性离散事件系统不变空间之间的对偶
4. SUFFICIENT CONDITION OF MAX-PLUS ELLIPSOIDAL INVARIANT SET AND COMPUTATION OF FEEDBACK CONTROL OF DISCRETE EVENT SYSTEMS [C] . Mourad Ahmane, Laurent Truffet International Conference on Informatics in Control, Automation and Robotics . 2006

机译：MAX-PLUS椭圆形不变集的充分条件和离散事件系统的反馈控制计算
5. Control-Parameter-Space Classification for Delay-Independent-Stability of Linear Time-Invariant Time-Delay Systems; Theory and Experiments. [D] . Nia, Payam Mahmoodi. 2014

机译：线性时不变时滞系统时滞稳定性的控制参数空间分类理论与实验。
6. Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control [O] . Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, -1

机译：控制非线性动力学系统的Koopman不变子空间和有限线性表示
7. Max-plus (A, B)-invariant spaces and control of timed discrete event systems [O] . Ricardo David Katz 2012

机译：最大加（A，B）不变空间和定时离散事件系统的控制

Max-Plus (A,B)-Invariant Spaces and Control of Timed Discrete-Event Systems

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