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Set inversion

In mathematics, set inversion is the problem of characterizing the preimage X of a set Y by a function f, i.e., X = f−1(Y ) = {x ∈ Rn | f(x) ∈ Y }. It can also be viewed as the problem of describing the solution set of the quantified constraint "Y(f (x))", where Y(y) is a constraint, e.g. an inequality, describing the set Y.

Example
The set X = f−1([4,9]) where f(x1, x2) = x + x is represented on the figure. 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. Since [−1,1]2 + [2,]2 = [0,1] + [4,5] = [4,6] is inside [4,9], we conclude that the whole box [−1,1] × [2,] is inside X. ==Application==
Application
Set inversion is mainly used for path planning, for nonlinear parameter set estimation, for localization or for the characterization of stability domains of linear dynamical systems. ==References==
Source: Wikipedia ↗
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