Reachability Analysis of Non-linear Planar Autonomous Systems

  • Hallstein Asheim Hansen
  • Gerardo Schneider
  • Martin Steffen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7141)


Many complex continuous systems are modeled as non-linear autonomous systems, i.e., by a set of differential equations with one independent variable. Exact reachability, i.e., whether a given configuration can be reached by starting from an initial configuration of the system, is undecidable in general, as one needs to know the solution of the system of equations under consideration.

In this paper we address the reachability problem of planar autonomous systems approximatively.We use an approximation technique which “hybridizes” the state space in the following way: the original system is partitioned into a finite set of polygonal regions where the dynamics on each region is approximated by constant differential inclusions. Besides proving soundness, completeness, and termination of our algorithm, we present an implementation, and its application into (classical) examples taken from the literature.


Hybrid System Autonomous System Lipschitz Constant Hybrid Automaton Reachability Analysis 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hallstein Asheim Hansen
    • 1
  • Gerardo Schneider
    • 2
    • 3
  • Martin Steffen
    • 3
  1. 1.Buskerud University CollegeKongsbergNorway
  2. 2.Chalmers University of GothenburgSweden
  3. 3.University of OsloNorway

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