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In this paper we propose a convex Sum-of-Squares optimization problem forfinding outer approximations of forward reachable sets for nonlinear uncertainOrdinary Differential Equations (ODE's) with either (or both) L2 or point-wisebounded input disturbances. To make our approximations tight we seek tominimize the volume of our approximation set. Our approach to volumeminimization is based on the use of a convex determinant-like objectivefunction. We provide several numerical examples including the Lorenz system andthe Van der Pol oscillator.

Using SOS and Sublevel Set Volume Minimization for Estimation of Forward Reachable Sets