MARCO: a reachability algorithm for multi-affine systems with applications to biological systems

Authors:
Spring Berman;Ádám Halász;Vijay Kumar
Affiliations:
GRASP Laboratory, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA;GRASP Laboratory, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA;GRASP Laboratory, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA
Venue:
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Year:
2007

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Abstract

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 multiaffine 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].