Geometrical approach to modeling of nonlinear systems from experimental data

Abstract

This monograph presents a geometric modeling method nonlinear dynamical systems from experimental data . basis method is a qualitative approach to the analysis of linear models and construction of the symmetry groups of attractors of dynamical systems with controls . A theoretical study including the central theorem manifold defining conditions of existence of the class in question models in the local area , taking into account the group properties , estimation algorithms invariant characteristics , methods of constructing models and identifiable description of the results obtained using the method for simulation -driven engineering processes . included two application is the development of the proposed approach : identification of groups symmetries on the phase portraits of dynamical systems and the method of constructing neural network predictive models