Epsilon-Approximation of Differential Inclusions

For a Lipschitz differential inclusion x ∈ f(x), we give a method to compute an arbitrarily close approimation of Reachf(X0, t) — the set of states reached after time t starting from an initial set X0. For a differential inclusion x ∈ f(x), and any e>0, we define a finite sample graph A∈. Every trajectory φ of the differential inclusion x ∈f(x) is also a “trajectory” in A∈. And every “trajectory” η of A∈ has the property that dist(ή(t), f(η(t))) ≤ e. Using this, we can compute the einvariant sets of the differential inclusion — the sets that remain invariant under e-perturbations in f.