Computational Approaches to Reachability Analysis of Stochastic Hybrid Systems

  • Alessandro Abate
  • Saurabh Amin
  • Maria Prandini
  • John Lygeros
  • Shankar Sastry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4416)

Abstract

This work investigates some of the computational issues involved in the solution of probabilistic reachability problems for discrete-time, controlled stochastic hybrid systems. It is first argued that, under rather weak continuity assumptions on the stochastic kernels that characterize the dynamics of the system, the numerical solution of a discretized version of the probabilistic reachability problem is guaranteed to converge to the optimal one, as the discretization level decreases. With reference to a benchmark problem, it is then discussed how some of the structural properties of the hybrid system under study can be exploited to solve the probabilistic reachability problem more efficiently. Possible techniques that can increase the scale-up potential of the proposed numerical approximation scheme are suggested.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Alessandro Abate
    • 1
  • Saurabh Amin
    • 1
  • Maria Prandini
    • 2
  • John Lygeros
    • 3
  • Shankar Sastry
    • 1
  1. 1.University of California, at Berkeley - Berkeley, CAUSA
  2. 2.Politecnico di Milano - MilanoItaly
  3. 3.ETH Zurich - ZurichSwitzerland

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