Identification of systems with fast and slow dynamics application to the cardiac action potential

This paper considers the parameter estimation problem for linear and nonlinear dynamical systems with slow and fast modes. First the identifiability property is investigated. Sufficient conditions on the local identifiability of the reduced system and of the boundary layer equation are given which insure the local identifiability of the initial perturbed system. Conditions allowing the separation of the identification problem into independent problems on the slow and fast modes are derived. In the general case, two level optimization procedures are proposed. An application of these algorithms to the parameter estimation of a model of cardiac action potential is presented.