  We propose a method to outer bound forward reachable sets on finite horizons
for uncertain nonlinear systems with polynomial dynamics. This method makes use
of time-dependent polynomial storage functions that satisfy appropriate
dissipation inequalities that account for time-varying uncertain parameters, L2
disturbances, and perturbations characterized by integral quadratic constraints
(IQCs) with both hard and soft factorizations. In fact, to our knowledge, this
is the first result introducing IQCs to reachability analysis, thus allowing
for various types of uncertainty, including unmodeled dynamics. The generalized
S-procedure and Sum-of-Squares techniques are used to derive algorithms with
the goal of finding the tightest outer bound with a desired shape. Both
pedagogical and practically motivated examples are presented, including a
7-state F-18 aircraft model.
