Functional analysis approach to the nonlinear stochastic dynamical systems

Abstract

In the paper general case of nonlinear stochastic dynamical system is considered. The sufficient conditions for robust application of the suggested method are proven with a theorem, applying the theory of nonlinear operators of the functional analysis. As a special case a model of a class of dynamical systems with nonlinear stochastic perturbation is also considered and the sufficient conditions for robust application of the suggested method are proven with the same theorem. An example for the latter case, comparing the numerical computer solution of the original system and the analytical solution of the approximate robust model are given. The method can be applied for analytical and computer modelling of nonlinear stochastic dynamical systems, optimization, synthesis of computer control and for investigation of the stochastic perturbation. © 2011 IEEE.