Reachability analysis of uncertain nonlinear systems using guaranteed set integration

In this paper we show how to compute the reachable space for uncertain nonlinear continuous dynamical systems by using guaranteed set integration. We introduce two ways to do so. The first one is a full interval method which handles whole domains for set computation and relies on Taylor series and interval analysis. The second one relies on the theory of monotone dynamical systems and can be used with cooperative systems only but makes it possible to bracket the uncertain nonlinear system between two nonlinear dynamical systems where there is no uncertainty. In most cases, the bracketing systems derived are piecewise differentiable functions, hence cannot be directly integrated via interval Taylor models. Our contribution resides then in the use of hybrid automata to model the bounding systems. We give examples which show the potentials of both approaches in presence of parameter and input uncertainties.