Choice of Directions for the Approximation of Reachable Sets for Hybrid Systems

  • Xin Chen
  • Erika Ábrahám
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6927)


In this paper we propose an approach to over-approximate the reachable set (with bounded time and number of transitions) of a hybrid system by a finite set of polytopes. The constraints of the polytope are determined by a direction choice method. For the hybrid systems whose (1) continuous dynamics are linear, (2) invariants and guards are defined by linear inequalities, and (3) variable resets are expressed by invertible affine maps, we show that the over-approximations can be computed in polynomial time, and the overestimation can be arbitrarily reduced by decreasing the discretization time step if the continuous dynamics are all deterministic. Some experimental results are also presented to show the effectiveness of our approach.


Convex Hull Hybrid System Linear Inequality Discrete Transition Hybrid Automaton 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xin Chen
    • 1
  • Erika Ábrahám
    • 1
  1. 1.RWTH Aachen UniversityGermany

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