On the computation of invariant sets for constrained nonlinear systems: An interval arithmetic approach

We present a method for the computation of the one-step set using interval arithmetic. The proposed specialized branch and bound algorithm provides an inner approximation with a given bound of the error; this makes it possible to achieve a trade off between accuracy of the computed set and computational burden. Furthermore an algorithm to approximate the one step set by an inner bounded polyhedron is also presented; this allows us to relax the complexity of the obtained set, and to make easier the recursion and storage of the sets.