# A RECENT DEVELOPMENT OF THE APPROACH ON THE ALGEBRAIC REPRESENTATION OF AFFINE CONTROL SYSTEMS. ALGEBRAIC CLASSIFICATION AND HOMOGENEOUS APPROXIMATION

16 janvier 2006, Salle R05, au Centre Automatique et Systèmes, Fontainebleau
14h : Grigory SKLYAR, IRCCYN et Univ. Szczecin, Pologne.
Analyzing the steering problem to the equilibrium for the affine control system we constructed the representation of the system as a series of nonlinear power moments. This representation is an analog of the Fliess representation of the Cauchy problem as a series of iterated integrals. Developing the algebraic approach proposed by M. Fliess we analyze some algebraic structures which the system generates in the algebra of nonlinear power moments and obtain a generalization of the remarkable R. Ree theorem. This allows, in particular, to give an algebraic classification of steering problems and to construct homogeneous approximations for affine control systems in a neighborhood of the equilibrium.