Dr. Colas Le Guernic (VERIMAG/CNRS, France)

 

Reachability Analysis of Hybrid Systems with Linear Continuous Dynamics

 

Abstract:

 

 This thesis is devoted to the problem of computing reachable sets
of linear and hybrid systems. In the first part, after exposing existing
approaches for reachability analysis of linear systems, we present the main
contribution of the thesis: a new algorithmic scheme for linear
time-invariant systems that definitely outperforms existing algorithms. As
the exact implementation furnishes a representation of the reachable sets
that is sometimes hard to manipulate, we propose an approximate version that
is not subject to the wrapping effect, an uncontrolled growth of the
approximation errors. We also discuss a variant of this algorithm
specialized to support functions, a functional representation of convex
sets. In the second part, we extend this work to hybrid systems. We first
show how to deal with the constraints on the continuous dynamics imposed by
the invariants. Then, we present algorithms for approximating the
intersection of the continuous reachable sets with hyperplanar guards.