On the asymptotic classification of nonlinear controlled systems in the neighborhood of the equilibrium

摘要

The problem of classification of nonlinear analytic control systems with respect to the asymp-totics of their controllability sets in a neighborhood of the equilibrium under different restrictions on the control is considered. The basis of our investigation is the analysis of special structures which are generated by the representation of systems in the form of series of nonlinear power moments. The restriction on the control generates the order relation between nonlinear power moments. From the algebraic point of view, this relation corresponds to the grading structure of the algebra of nonlinear power moments.