Diffusive Identification of Volterra Models by Cancellation of the Nonlinear Term

Abstract

We present a new identification method for nonlinear Volterra models of the form HX = F (u, X) + v with H a causal convolution operator. It is based first on a suitable parameterization of H 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(∂ t ) alone. Then, the nonlinear term can be identified from standard regression methods. For illustration, we implement this method on a concrete numerical example.

System identification by operatorial cancellation of nonlinear terms and application to a class of Volterra models

“…The application of operator D x;0 to equation (1) leads to the restriction of model (42) to the subsets i;j x;0 , whose interest comes from the following property of operator D x;0 :…”

“…The identification model considered is the one described in Example 2.4 (and in [30]). For an other concrete example of application, see [42] in which the identification method has been applied to the model of the spherical flame described in Example 2.3. 6.4.1.…”

Identification of Time-non local Models under Diffusive Representation

“…Second, this method can also be used when the function f changes from one data set to the other. This identification method is still under study: more information about it will be found in (Casenave and Montseny [2009a]). …”