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

摘要

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 rect-angular 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].