Algebraic identification problem: results and perspectives (Q5959712)

The input-output behavior of nonlinear analytical dynamical systems can be encoded symbolically in a noncommutative formal power series (as shown by M. Fliess). For nonlinear dynamical systems this gives an equivalent of the Laplace transform. The authors consider the inverse problem: for a given input/output behavior, effectively compute its symbolic description starting from some finite panels of input/output data. Several ways for effective computation of the terms of generating series are presented (in the case of numerically exact data). A commutative approach based on the representation of the output as an analytic expansion on the basis of the shuffle algebra is first presented. Then a combinatorial approach based on the analysis of recurrence relationships via Chen series and its successive derivatives is developed. No application is given at this time.