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MARCO: A Reachability Algorithm for Multi-affine Systems with Applications to Biological Systems

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 4416)


We present a new algorithm for the reachability analysis of multi-affine hybrid systems. In our previous work on reachability analysis and that of our collaborators [1,2,3], we exploited the convexity of multi-affine functions and the fact that the vector field in modes with rectangular invariants is uniquely determined by its values at the rectangle vertices. In this paper, we explicitly calculate conical overapproximations of the reachable set in the invariant of each mode. We describe our Multi-Affine Reachability analysis using Conical Overapproximations, Marco, and show that it yields results that are superior to those obtained by existing methods for multi-affine hybrid systems. Finally, we demonstrate the application of Marco to the analysis of an ant house hunting model that incorporates quorum sensing [4] and the analysis of bi-stability of the lactose induction system regulated by glucose and lactose [5].


  • Hybrid System
  • Hybrid Automaton
  • Reachability Analysis
  • Reachability Problem
  • Bistability Region

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Berman, S., Halász, Á., Kumar, V. (2007). MARCO: A Reachability Algorithm for Multi-affine Systems with Applications to Biological Systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds) Hybrid Systems: Computation and Control. HSCC 2007. Lecture Notes in Computer Science, vol 4416. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71492-7

  • Online ISBN: 978-3-540-71493-4

  • eBook Packages: Computer ScienceComputer Science (R0)