Discrete-Time Nonlinear Singularly Perturbed System Identification Using Coupled Multimodel Representation

Many control and observability theories for singularly perturbed systems require the full knowledge of system model parameters exceptionally if the system is considered as black box. To overcome this problem and to obtain an accurate and faithful model, this paper describes a new identification method for discrete-time nonlinear singularly perturbed systems (NLSPS) using the coupled state multimodel representation. The Levenberg-Marquardt algorithm is used to identify not only the submodels parameters but also the perturbation parameter epsilon. Two cases are considered to identify these systems. The first one supposes that the perturbation parameter epsilon of the real system is known and thus only the submodels parameters are identified. The second case supposes that this perturbation parameter is unknown and has to be identified with the other submodels parameters. The simulation example demonstrates the effectiveness of the proposed identification.