Séance Séminaire

Séminaire ACSIOM

Diffusive representation and application to the analysis and the resolution of non local dynamic problems

In lots of dynamic systems of Physics or others scientific fields such as Biology, dynamic integral operators, often of convolution type, are involved. Contrary to the standard case of differential models, problems relating to integro-differential models are often difficult to solve, especially because these models are not time-local.In this context, the methodology called “diffusive representation” presents some interests: an integral operator is represented by its gamma-symbol, directly deduced from its transfer function, and can be formulated by means of a state realisation whose dimension is numerically reasonable whatever the size of the system may be. In addition to this interesting practical side, the diffusive representation offers a unified mathematical framework, well adapted to analysis of integral convolution operators. The first part of the talk will be an introduction to the diffusive representation, the principle and the main results of which will be given. The second part will deal with some dynamic problems which can be tackled in an original and quite simple way by using the diffusive representation. In fact, all the operatorial problems of modeling, simulation, control, model identification, model reduction, etc. can be formulated in such a way that the object of the problem is the gamma-symbol of the operator solution. (Le séminaire sera en français)