Set inversion

When f is nonlinear the set inversion problem can be solved[1] using interval analysis combined with a branch-and-bound algorithm.

[2] The main idea consists in building a paving of Rp made with non-overlapping boxes.

The algorithm can be made more efficient by replacing the inclusion tests by contractors.

For instance, since [−2,1]2 + [4,5]2 = [0,4] + [16,25] = [16,29] does not intersect the interval [4,9], we conclude that the box [−2,1] × [4,5] is outside X.

Set inversion is mainly used for path planning, for nonlinear parameter set estimation,[3][4] for localization[5][6] or for the characterization of stability domains of linear dynamical systems.