Reachability analysis for nonlinear systems by guaranteed piecewise affine approximation

In this paper, we present an approach able to analysis reachability of non-linear hybrid systems. Using the hybridization method, it is possible to construct an approximation of the non-linear systems, in the form of piecewise affine systems with uncertainties, for which efficient approaches for computing reachability have been proposed. To do this, we first generate a partition of the state space of the nonlinear system. Then, we approximate locally, in each element of this partition, the non-linear system by an affine one. Finally, we add the approximation error in the affine model. In this way, instead of studying a complex non-linear systems we study locally an affine system with uncertainty.