  Modern control-command systems often include controllers that perform
nonlinear computations to control a physical system, which can typically be
described by an hybrid automaton containing high-dimensional systems of
nonlinear differential equations. To prove safety of such systems, one must
compute all the reachable sets from a given initial position, which might be
uncertain (its value is not precisely known). On linear hybrid systems,
efficient and precise techniques exist, but they fail to handle nonlinear flows
or jump conditions. In this article, we present a new tool name HySon which
computes the flowpipes of both linear and nonlinear hybrid systems using
guaranteed generalization of classical efficient numerical simulation methods,
including with variable integration step-size. In particular, we present an
algorithm for detecting discrete events based on guaranteed interpolation
polynomials that turns out to be both precise and efficient. Illustrations of
the techniques developed in this article are given on representative examples.
