Citation
Haiyang Zheng, Edward A. Lee, Aaron Ames. "Beyond Zeno: Get on with It!". Joao Hespanha, Ashish Tiwari (eds.), 568-582, 3927, Springer Berlin/Heidelberg, 2006; From "Hybrid Systems: Computation and Control, Proceedings". 3927, ISBN: 3-540-33170-0.

Abstract
In this paper we propose a technique to extend the simulation of a Zeno hybrid system beyond its Zeno time point. A Zeno hybrid system model is a hybrid system with an execution that takes an infinite number of discrete transitions during a finite time interval. We argue that the presence of Zeno behavior indicates that the hybrid system model is incomplete by considering some classical Zeno models that incompletely describe the dynamics of the system being modeled. This motivates the systematic development of a method for completing hybrid system models through the introduction of new post-Zeno states, where the completed hybrid system transitions to these post-Zeno states at the Zeno time point. In practice, simulating a Zeno hybrid system is challenging in that simulation effectively halts near the Zeno time point. Moreover, due to unavoidable numerical errors, it is not practical to exactly simulate a Zeno hybrid system. Therefore, we propose a method for constructing approximations of Zeno models by leveraging the completed hybrid system model. Using these approximation, we can simulate a Zeno hybrid system model beyond its Zeno point and reveal the complete dynamics of the system being modeled.

Electronic downloads

• http://ptolemy.eecs.berkeley.edu/publications/papers/06/beyondZeno/
• http://dx.doi.org/10.1007/11730637

• HTML

  Haiyang Zheng, Edward A. Lee, Aaron Ames. <a
  href="http://chess.eecs.berkeley.edu/pubs/46.html"
  ><i>Beyond Zeno: Get on with
  It!</i></a>, Joao Hespanha, Ashish Tiwari
  (eds.), 568-582, 3927, Springer Berlin/Heidelberg, 2006;
  From "Hybrid Systems: Computation and Control,
  Proceedings". 3927, ISBN: 3-540-33170-0.

• Plain text

  Haiyang Zheng, Edward A. Lee, Aaron Ames. "Beyond Zeno:
  Get on with It!". Joao Hespanha, Ashish Tiwari (eds.),
  568-582, 3927, Springer Berlin/Heidelberg, 2006; From
  "Hybrid Systems: Computation and Control,
  Proceedings". 3927, ISBN: 3-540-33170-0.

• BibTeX

  @inbook{ZhengLeeAmes06_BeyondZenoGetOnWithIt,
      author = {Haiyang Zheng and Edward A. Lee and Aaron Ames},
      editor = {Joao Hespanha, Ashish Tiwari},
      title = {Beyond Zeno: Get on with It!},
      pages = {568-582},
      volume = {3927},
      publisher = {Springer Berlin/Heidelberg},
      year = {2006},
      note = {From "Hybrid Systems: Computation and Control,
                Proceedings". 3927, ISBN: 3-540-33170-0},
      abstract = {In this paper we propose a technique to extend the
                simulation of a Zeno hybrid system beyond its Zeno
                time point. A Zeno hybrid system model is a hybrid
                system with an execution that takes an infinite
                number of discrete transitions during a finite
                time interval. We argue that the presence of Zeno
                behavior indicates that the hybrid system model is
                incomplete by considering some classical Zeno
                models that incompletely describe the dynamics of
                the system being modeled. This motivates the
                systematic development of a method for completing
                hybrid system models through the introduction of
                new post-Zeno states, where the completed hybrid
                system transitions to these post-Zeno states at
                the Zeno time point. In practice, simulating a
                Zeno hybrid system is challenging in that
                simulation effectively halts near the Zeno time
                point. Moreover, due to unavoidable numerical
                errors, it is not practical to exactly simulate a
                Zeno hybrid system. Therefore, we propose a method
                for constructing approximations of Zeno models by
                leveraging the completed hybrid system model.
                Using these approximation, we can simulate a Zeno
                hybrid system model beyond its Zeno point and
                reveal the complete dynamics of the system being
                modeled.},
      URL = {http://chess.eecs.berkeley.edu/pubs/46.html}
  }
  

Posted by Mary Stewart on 4 May 2006.
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