Identification of non linear fractional systems using continuous time neural networks

François Benoit-Marand (1) , Laurent Signac (1) , Thierry Poinot (1) , Jean-Claude Trigeassou (1)

1 LAII [Poitiers] - Laboratoire d'automatique et d'informatique industrielle [EA 1219]

Fractional systems allow us to model the processes governed by a diffusive equation. The simulation of such processes can be realized by using a non integer integrator. The aim of this paper is to estimate, in the time domain, both the non integer derivative order and the physical law of a non linear fractional system. To achieve this goal, we use Continuous Time Neural Networks. CTNN are dynamical neural structures that differ from the classical recurrent neural networks on the use of integrator blocks rather than delay blocks. This difference allows us to access the physical law of the system rather than only having a black box model. A non-integer CTNN is composed of a neural network and a non integer integrator. The identification stage - which consists in finding the good parameters for the neural network and for the integrator block- will be performed by using an output error identification. At the end of the procedure, a model reduction stage can be performed in order to revert from the neural network to a more realistic expression of the physical law of the process. To illustrate the method we'll give some simulation results.

Mots clés: Neural networks; Non integer integrator; Non linear fractional systems; Output error identificatio

Domaines: Réseau de neurones [cs.NE]; Automatique

François Benoit-Marand, Laurent Signac, Thierry Poinot, Jean-Claude Trigeassou. Identification of non linear fractional systems using continuous time neural networks. lFAC Workshop on Fractional Differentiation and its Applications, Jul 2006, Porto, Portugal. vol2 part1. ⟨hal-00211783⟩