ε-Approximation of differential inclusions

Abstract

For a Lipschitz differential inclusion x ∈ f(x), we give a method to compute an arbitrarily close approimation of Reach _f(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 ε>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))) ≤ ε. Using this, we can compute the εinvariant sets of the differential inclusion — the sets that remain invariant under ε-perturbations in f.

Research supported by the California PATH program and by the National Science Foundation under grant ECS9417370.