In this paper, we investigate nonlinear reachability computation in presence of model uncertainty, via guaranteed set integration. We show how this can be done by using the classical Mueller's existence theorem. The core idea developed is to no longer deal with whole sets but to derive instead two nonlinear dynamical systems which involve no model uncertainty and which bracket in a guaranteed way the space reachable by the original uncertain system. We give a rule for building the bracketing systems. In the general case, the bracketing systems obtained are only piecewise C~k-continuously differential nonlinear systems and hence can naturally be modeled with hybrid automata. We show how to derive the hybrid model and how to address mode switching. An example is given with a biological process.
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