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Accurate Event Detection for Simulating Hybrid Systems

  • Joel M. Esposito
  • Vijay Kumar
  • George J. Pappas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2034)

Abstract

It has been observed that there are a variety of situations in which the most popular hybrid simulation methods can fail to properly detect the occurrence of discrete events. In this paper, we present a method for detecting discrete which, using techniques borrowed from control theory, selects integration step sizes in such a way that the simulation slows down as the state approaches a set which triggers an event (a guard set). Our method guarantees that the state will approach the boundary of this set exponentially; and in the case of linear or polynomial guard descriptions, terminating on it, without entering it. Given that any system with a nonlinear guard description can be transformed to an equivalent system with a linear guard description, this technique is applicable to a broad class of systems. Even in situations where nonlinear guards have not been transformed to the canonical form, the method is still increases the chances of detecting and event in practice. We show how to extend the method to guard sets which are constructed from many simple sets using boolean operators (e.g. polyhedral or semi-algebraic sets). The technique is easily used in combination with existing numerical integration methods and does not adversely affect the underlying accuracy or stability of the algorithms.

Keywords

Hybrid System Taylor Series Expansion Link Manipulator Hybrid Automaton Positive Real Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Joel M. Esposito
    • 1
  • Vijay Kumar
    • 1
  • George J. Pappas
    • 2
  1. 1.MEAM DepartmentUniversity of PennsylvaniaPhiladelphia
  2. 2.EE DepartmentUniversity of PennsylvaniaPhiladelphia

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