Diffusive Identification of Volterra Models by Cancellation of the Nonlinear Term

International audienceWe present a new identification method for nonlinear Volterra models of the form H(dt)X=F(u,X)+v with H(dt) a causal convolution operator. It is based first on a suitable parameterization of H(dt) deduced from the so-called diffusive representation, devoted to state representations of integral operators, and second on a suitable operatorial transformation of the problem with the property that the nonlinear term F(u,X) is cancelled, allowing to identify the operator H(dt) alone. Then, the nonlinear term can be identified from standard regression methods. For illustration, we implement this method on a concrete numerical example