Artificial Perturbation Method for Nonlinear Dynamical Systems and its Computational Applications

Abstract

In the paper a perturbation method and robust approximation model of nonlinear dynamical systems, using sequence of time-invariant linear systems are applied. The sufficient conditions for robust application of the perturbation method and the validity of the approximation are proven with a theorem, applying the theory of nonlinear operators of the functional analysis. Three examples comparing the numerical solution of the original system and the analytical solution of the approximate robust model are given. The method can be applied for analysis of dynamical systems, complex systems, optimization, synthesis of computer control and for investigation of classical perturbation problems.