Time-local formulation and identification of implicit Volterra models by use of diffusive representation

We present a time-continuous identification method for nonlinear dynamic Volterra models of the form HX = f(u,X)+v with H a causal convolution operator. It is mainly based on a suitable parameterization of H deduced from the so-called diffusive representation, which is devoted to state representations of integral operators. Following this approach, the complex dynamic nature of H can be summarized by a few numerical parameters on which the identification of the dynamic part of the model will focus. The method is validated on a physical numerical example.