Kamel Abderrahim

A new recursive algorithm for simultaneous identification of discrete time delay systems

Abstract A new algorithm for simultaneous online identification of unknown time delay and parameters of discrete-time delay systems is proposed in this paper. This algorithm consists in constructing a linear-parameters formulation and using the recursive least squares approach to solve the obtained system. Simulation example and experimental test results are presented to illustrate the performance of the proposed approach.

Hierarchical gradient based identification of discrete-time delay systems

In this paper, we apply a hierarchical identification principle to identify simultaneously the unknown time delay and dynamic parameters of discrete-time delay systems. In our approach, we separate the nonlinear cost function into two simple cost functions and present a gradient iterative algorithm for estimating directly the time delay and the parameters. The cost function used to estimate the time delay is an integer nonlinear programming problem (IP) and the solution of the integer version of a nonlinear optimization problem is obtained by rounding the solution for its continuous relaxation (CP). Furthermore, we give an appropriate choice of the convergence factor. Finally, the effectiveness of this method has been illustrated through simulation.

Neural emulation applied to chemical reactors

In this paper, a real time recurrent learning-based emulator is presented for nonlinear plants with unknown dynamics. This emulator is based on fully connected recurrent neural networks. Starting from zero values, updating rate, time parameter and weights of the instantaneous neural emulator adapt themselves in order to estimate the process output. The contribution of this paper is to validate the emulator with experimental data from the batch reactor of National Engineering School of Gabes, Tunisia.

New Approaches to Identification of PWARX Systems

We consider the clustering-based procedures for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. These methods exploit three main techniques which are clustering, linear identification, and pattern recognition. The clustering method based on the -means algorithm is treated in this paper. It consists in estimating both the parameter vector of each submodel and the coefficients of each partition while knowing the model orders and and the number of submodels . The performance of this approach can be threatened by the presence of outliers and poor initializations. To overcome these problems, we propose new techniques for data classification. The proposed techniques exploit Chiu’s clustering technique and the self-artificial Kohonen neural network approach in order to improve the performance of both the clustering and the final linear regression procedure. Simulation results are presented to illustrate the performance of the proposed method.

Online Identification of Multivariable Discrete Time Delay Systems Using a Recursive Least Square Algorithm

This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.

Nonlinear approach for the identification of discrete time delay systems

A new approach for simultaneous recursive identification of an unknown time delay of discrete-time delay systems is proposed in this paper. The proposed Levenberg-Marquardts algorithm is used to deal with the identification problem. The effectiveness of this method has been illustrated through simulation.

A numerical approach for performance analysis of higher-order statistics based identification methods

This paper addresses the problem of performance analysis of linear algebra methods for higher-order statistics based identification. We propose another approach which can be used to evaluate the performance of these methods. This approach is based on the use of the condition number of system of equations. To illustrate the effectiveness of our approach, several simulation examples are presented.

Identification of non-minimum phase finite impulse response systems using the fourth-order cumulants

We have presented two contributions for identification of LTI NMP FIR systems. They use the fourth order cumulants of the noisy observations of the system output and consequently yield consistent parameters estimation in the presence of additive Gaussian noise. Both recursive closed-form and batch least squares solutions of the parameters estimation are proposed for each contribution. The second contribution allows to reduce the redundancy of the vector of unknown parameters is developed. Finally, the simulation results showed that the performance of our contributions is better than the other methods.

A robust reduced order functional H ∞ observer for time delay bilinear systems

This paper proposes a method for the design of a robust functional H∞ observer for a class of time delay bilinear systems. The considered system is affected by norm-bounded uncertainties in the system matrices and an unmeasured perturbations which are of finite energy. The unbiasedness conditions on the nominal part of the error dynamics of the proposed reduced order observer were given by calling an algebraic framework. Since, those conditions are satisfied, and by calling a Lyapunov-krasovskii approach, the stability conditions are obtained through LMI (Linear Matrix Inequality).

Recursive blind equalization for the bounded noise case under different modulations

In this paper, the blind equalization problem in presence of bounded noise with different modulations (QAM, PSK and ASK) is addressed. A first blind equalization algorithm is reminded, then an extension is proposed. Few synthesis parameters have to be fixed by the user in the proposed approach. In order to illustrate the efficiency of the proposed algorithm, we compare with another well known existing technique. Simulation results prove the good performance of the proposed algorithm.