  To verify the correct operation of systems, engineers need to determine the
set of configurations of a dynamical model that are able to safely reach a
specified configuration under a control law. Unfortunately, constructing models
for systems interacting in highly dynamic environments is difficult. This paper
addresses this challenge by presenting a convex optimization method to
efficiently compute the set of configurations of a polynomial hybrid dynamical
system that are able to safely reach a user defined target set despite
parametric uncertainty in the model. This class of models describes, for
example, legged robots moving over uncertain terrains. The presented approach
utilizes the notion of occupation measures to describe the evolution of
trajectories of a nonlinear hybrid dynamical system with parametric uncertainty
as a linear equation over measures whose supports coincide with the
trajectories under investigation. This linear equation with user defined
support constraints is approximated with vanishing conservatism using a
hierarchy of semidefinite programs that are each proven to compute an
inner/outer approximation to the set of initial conditions that can reach the
user defined target set safely in spite of uncertainty. The efficacy of this
method is illustrated on a collection of six representative examples.
