Journal of Computing Science and Engineering

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Ensuring Sound Numerical Simulation of Hybrid Automata

  • Hur, Yerang (Department of Computer and Information Science, University of Pennsylvania) ;
  • Sim, Jae-Hwan (Department of Computer Science and Engineering, Korea University) ;
  • Kim, Je-Sung (Department of Computer and Information Science, University of Pennsylvania) ;
  • Chai, Jin-Young (Department of Computer Science and Engineering, Korea University)
  • Published : 2009.06.30
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Abstract

A hybrid system is a dynamical system in which states can be changed continuously and discretely. Simulation based on numerical methods is the widely used technique for analyzing complicated hybrid systems. Numerical simulation of hybrid systems, however, is subject to two types of numerical errors: truncation error and round-off error. The effect of such errors can make an impossible transition step to become possible during simulation, and thus, to generate a simulation behavior that is not allowed by the model. The possibility of an incorrect simulation behavior reduces con.dence in simulation-based analysis since it is impossible to know whether a particular simulation trace is allowed by the model or not. To address this problem, we define the notion of Instrumented Hybrid Automata (IHA), which considers the effect of accumulated numerical errors on discrete transition steps. We then show how to convert Hybrid Automata (HA) to IRA and prove that every simulation behavior of IHA preserves the discrete transition steps of some behavior in HA; that is, simulation of IHA is sound with respect to HA.

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References

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