Reachability of Weakly Nonlinear Systems Using Carleman Linearization

In this article we introduce a solution method for special class of nonlinear initial-value problems using set-based propagation techniques. The novelty the approach is that employ particular embedding (Carleman linearization) to leverage recent advances high-dimensional reachability solvers linear ordinary differential equations based on support function. Using global error bound Carleman linearization abstraction, are able describe full set behaviors system sets initial conditions and in dense time.