Kamel Abderrahim

For the fractional-order Hammerstein system with white noise, the difficulty of identification is that the parameters of the linear and the nonlinear blocks and the fractional order are unknown and the intermediate variable and the states are unmeasurable. To overcome this difficulty, we transform the system from an input nonlinear pseudo-state-space system to an input–output representation and we develop an algorithm based on the Recursive Least Squares, the Levenberg–Marquardt and the Auxiliary Model Principle. The convergence of the identified parameters is studied. The performance of the proposed algorithm are tested by two numerical examples.

This paper addresses the problem of the design of an adaptive observer for a class of time delay systems, in order to give a suitable estimation of the system states and its unknown parameters simultaneously. Based on a descriptor LPV system approach, we propose a simple full order adaptive observer via Linear Matrix Inequalities (LMI's). Those LMI's permit to fulfill the conditions of the estimation errors stability, relying on Krasovskii Lyapunov approach for time delay systems.

In this paper, a new approach which serves firstly the estimation of the actuator fault and secondly its compensation for hybrid switched system is presented. The compensation of this fault is based on the use of the additive fault tolerant control. So, this paper extends an estimation method (Data-based Projection Method) for switched system to estimate the actuator fault. Then, the additive control is synthesized by exploitation the fault estimation. So, the additive fault tolerant control is obtained by combining this additive control to the nominal control. The efficiency of this method has been demonstrated by an example.

In this paper the problem of identifying PieceWise AutoRegressive eXogenous (PWARX) systems is treated. Only the clustering based methods are considered. It consists in estimating both the parameter vector of each sub-model and the coefficients of each partition while knowing the model orders and the number of sub-models. We compare the k-means based methods with two recently proposed methods: the Chiu's clustering method and the Kohonen Neural Network based method. Simulation results are presented to illustrate the performance of the proposed methods.