Approximation of General Stochastic Hybrid Systems by Switching Diffusions with Random Hybrid Jumps

  • Alessandro Abate
  • Maria Prandini
  • John Lygeros
  • Shankar Sastry
Conference paper

DOI: 10.1007/978-3-540-78929-1_43

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4981)
Cite this paper as:
Abate A., Prandini M., Lygeros J., Sastry S. (2008) Approximation of General Stochastic Hybrid Systems by Switching Diffusions with Random Hybrid Jumps. In: Egerstedt M., Mishra B. (eds) Hybrid Systems: Computation and Control. HSCC 2008. Lecture Notes in Computer Science, vol 4981. Springer, Berlin, Heidelberg

Abstract

In this work we propose an approximation scheme to transform a general stochastic hybrid system (SHS) into a SHS without forced transitions due to spatial guards. Such switching mechanisms are replaced by spontaneous transitions with state-dependent transition intensities (jump rates). The resulting switching diffusion process with random hybrid jumps is shown to converge in distribution to the original stochastic hybrid system execution. The obtained approximation can be useful for various purposes such as, on the computational side, simulation and reachability analysis, as well as for the theoretical investigation of the model. More generally, it is suggested that SHS which are endowed exclusively with random jumping events are simpler than those that present spatial forcing transitions.

In the opening of this work, the general SHS model is presented, a few of its basic properties are discussed, and the concept of generator is introduced. The second part of the paper describes the approximation procedure, introduces the new SHS model, and proves, under some assumptions, its weak convergence to the original system.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Alessandro Abate
    • 1
  • Maria Prandini
    • 2
  • John Lygeros
    • 3
  • Shankar Sastry
    • 1
  1. 1.University of California, BerkeleyBerkeleyUSA
  2. 2.Politecnico di MilanoMilanoItaly
  3. 3.ETH ZurichZurichSwitzerland

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