The Generalized Normal Forms and Method of Resonance Control of Nonlinear Dynamical Systems

Abstract

This paper addresses a new method (named the generalized normal forms (GNF) method) which allows one to find normal forms for the broad class of dynamical systems not considered by earlier techniques. The proposed method is feasible for the dynamical systems with non-smooth and discontinuous non-linearity. The GNF method overcomes the lack of computability of earlier techniques. It is based on a simple iterative procedure which leads to an effective computer algorithm. The GNF method has been implemented in computer software which becomes a convenient tool for both qualitative and numerical analysis. The GNF method is applied to design a resonance stabilization feedback control for a critical nonlinear system. The method of resonance control here developed allows one both to find an efficient stabilization feedback and to estimate the basin of attractor.