  In this paper we propose a convex Sum-of-Squares optimization problem for
finding outer approximations of forward reachable sets for nonlinear uncertain
Ordinary Differential Equations (ODE's) with either (or both) L2 or point-wise
bounded input disturbances. To make our approximations tight we seek to
minimize the volume of our approximation set. Our approach to volume
minimization is based on the use of a convex determinant-like objective
function. We provide several numerical examples including the Lorenz system and
the Van der Pol oscillator.
