Towards a geometric theory of hybrid systems

被引：0
|
作者：
Simic, SN [1 ]
Johansson, KH
Lygeros, J
Sastry, S
机构：
[1] San Jose State Univ, Dept Math, San Jose, CA 95192 USA
[2] Royal Inst Technol, Dept Signals Sensors & Syst, S-10044 Stockholm, Sweden
[3] Univ Patras, Dept Elect & Comp Engn, GR-26500 Patras, Greece
[4] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA
来源：
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES B-APPLICATIONS & ALGORITHMS | 2005年 / 12卷 / 5-6期
关键词：
hybrid system; dynamical system; hybrifold; Zeno; topological equivalence;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose a framework for a geometric theory of hybrid systems. Given a deterministic, non-blocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally non-smooth) dynamical systems. This point of view is adopted in studying the Zeno phenomenon. We show that it is due to nonsmoothness of the hybrid flow. We introduce the notion of topological equivalence of hybrid systems and locally classify isolated Zeno states in dimension two.
引用
收藏
页码：649 / 687
页数：39
相关论文
共 50 条
  • [1] Towards a geometric theory of hybrid systems
    Simic, SN
    Johansson, KH
    Sastry, S
    Lygeros, J
    [J]. HYBRID SYSTEMS: COMPUTATION AND CONTROL, 2000, 1790 : 421 - 436
  • [2] Towards a theory of stochastic hybrid systems
    Hu, JH
    Lygeros, J
    Sastry, S
    [J]. HYBRID SYSTEMS: COMPUTATION AND CONTROL, 2000, 1790 : 160 - 173
  • [3] Towards a stability theory of general hybrid dynamical systems
    Michel, AN
    Hu, B
    [J]. AUTOMATICA, 1999, 35 (03) : 371 - 384
  • [4] Hybrid geometric reduction of hybrid systems
    Ames, Aaron D.
    Sastry, Shankar
    [J]. PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, : 923 - 929
  • [5] Towards a geometric theory for left loops
    Baez, Karla
    [J]. COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2014, 55 (03): : 315 - 323
  • [6] Geometric control of hybrid systems?
    Legat, Benoit
    Jungers, Raphael M.
    [J]. NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2023, 47
  • [7] Geometric analysis of nondeterminacy in dynamical systems - Towards a geometric analysis of concurrent systems
    Wisniewski, Rafael
    Raussen, Martin
    [J]. ACTA INFORMATICA, 2007, 43 (07) : 501 - 519
  • [8] TOWARDS A THEORY OF SYSTEMS
    SAHAL, D
    [J]. GENERAL SYSTEMS, 1977, 22 : 41 - 55
  • [9] GEOMETRIC STRUCTURES IN SYSTEMS-THEORY
    CROUCH, PE
    [J]. IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS, 1981, 128 (05): : 242 - 251
  • [10] Towards Geometric Completion of Differential Systems by Points
    Wu, Wenyuan
    Reid, Greg
    Golubitsky, Oleg
    [J]. APPROXIMATE COMMUTATIVE ALGEBRA, 2009, : 79 - +
12345