Taylor Approximation for Hybrid Systems

Wepropose a new approximation technique forHybridAutomata. Given anyHybridAutomatonH, we callApprox(H , k) the Polynomial Hybrid Automaton obtained by approximating each formula in H with the formulae k obtained by replacing the functions in with their Taylor polynomial of degree k. We prove that Approx(H , k) is an over-approximation ofH. We study the conditions ensuring that, given any > 0, some k0 exists such that, for all k > k0, the “distance” between any vector satisfying k and at least one vector satisfying is less than . We study also conditions ensuring that, given any > 0, some k0 exists such that, for all k > k0, the “distance” between any configuration reached by Approx(H , k) in n steps and at least one configuration reached by H in n steps is less than . © 2007 Elsevier Inc. All rights reserved.