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

Abstract

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

Robust PI multiobserver for discrete nonlinear singularly perturbed system with unmeasurable premise variables

“…In this article, we are interested to discrete-time nonlinear SPS subject to disturbances and noises. Generally, these systems can be represented by two different models 4,21 Model 1:…”

“…The presence of a small parameter ε called singular perturbation parameter, which determines the degree of separation between slow and fast dynamics, makes the analysis of this kind of system complex. 1–4 As the identification, the control, and the diagnosis of nonlinear SPSs require knowledge of all state variables, which are not always measurable, the issue of nonlinear SPS state estimation has been a critical research topic over the last few decades, especially in the presence of disturbances and noises. The problem of the state estimation of these systems becomes more and more complex with the existence of nonlinearities and the presence of disturbances and noises.…”

“…In Rajab et al, 23 a decoupled multimodel predictive control for discrete-time nonlinear SPS has been investigated. The coupled state structure has been proposed in Asma et al 4 and Rakia et al 21 for nonlinear SPSs. In these works, the coupled structure is characterized by a global state x that couples all the submodels and a common perturbation parameter for all the submodels.…”

“…In these works, the coupled structure is characterized by a global state x that couples all the submodels and a common perturbation parameter for all the submodels. The coupled state MM structure for nonlinear SPSs can be generated using either the identification technique (based on a set of identified data derived from the real system) 4 or the Convex Polytopic Transformation (CPT) technique. 21 As a result, the linear SPSs state estimation theory can be applied to the analysis and synthesis of nonlinear SPSs.…”

“…[18][19][20] Recently, these techniques have been used to represent and control nonlinear SSPs with and without delay. 4,[21][22][23] The decoupled state MM structure has been investigated in Asma et al 22 to solve the identification problem for discrete nonlinear SPSs. Indeed, the nonlinear SPSs are represented using a set of local linear SPS submodels that are perfectly decoupled (each model has its own state vector and its own singular perturbation parameter).…”