Hassani Messaoud

Online identification of nonlinear system using reduced kernel principal component analysis

The Principal Component Analysis (PCA) is a powerful technique for extracting structure from possibly high-dimensional data sets. It is readily performed by solving an eigenvalue problem, or by using iterative algorithms that estimate principal components. This paper proposes a new method for online identification of a nonlinear system modelled on Reproducing Kernel Hilbert Space (RKHS). Therefore, the PCA technique is tuned twice, first we exploit the Kernel PCA (KPCA) which is a nonlinear extension of the PCA to RKHS as it transforms the input data by a nonlinear mapping into a high-dimensional feature space to which the PCA is performed. Second, we use the Reduced Kernel Principal Component Analysis (RKPCA) to update the principal components that represent the observations selected by the KPCA method.

Online prediction model based on the SVD-KPCA method.

This paper proposes a new method for online identification of a nonlinear system modelled on Reproducing Kernel Hilbert Space (RKHS). The proposed SVD-KPCA method uses the Singular Value Decomposition (SVD) technique to update the principal components. Then we use the Reduced Kernel Principal Component Analysis (RKPCA) to approach the principal components which represent the observations selected by the KPCA method.

A new online fault detection method based on PCA technique

In this paper, we suggest an extension of a previous study in Recursive Singular Spectrum Analysis (RSSA) (Hongli & Hui-Jun (2012) Fault detection for Markovian jump systems with sensor saturations and randomly varying non-linearities. IEEE Trans. Circuits Syst. I: Regul. Pap., 59, 2354–2362) to an online method for fault detection. This extended method is based on first-order perturbation (FOP) theory where the eigenvalues and eigenvectors of the foregoing covariance matrix are updated taking into account the effect of new acquired data which are considered as perturbation in the actual covariance matrix. This proposed diagnosis method is entitled ‘recursive principal component analysis based on FOP’ (RPCA-FOP) and is compared with other PCA techniques existing in literature such as the conventional PCA and the sliding window PCA where the average computation time, the missed detection rate and the false alarm rate are evaluated for each method.

Exponential Observer for a Class of One-Sided Lipschitz Stochastic Nonlinear Systems

This note investigates observer design for a class of nonlinear one-sided Lipschitz stochastic systems with multiplicative noises. It is shown that the almost sure exponential convergence of the observation error could be treated by decoupling the state from this error. This is done by using a new theorem dedicated to triangular stochastic systems. The observer gains are designed using a polytopic technique exploiting the structure of the control inputs, coupled with a descriptor systems approach.

Unknown inputs functional observers designs for delay descriptor systems

New time and frequency domain designs of unknown inputs functional observers (UIFO) for a class of descriptor systems with a constant time delay are investigated in this paper. The unknown inputs are present in both the state and the measurement equations. The time procedure design is based on the unbiasedness of the estimation error and the Lyapunov Krasovskii stability theory. After given the existence condition of such observers, the gain implemented in the functional observer with internal delay design is obtained in terms of linear matrix inequalities. The particular cases, where the observer is independent of internal delay and where it is independent of delay are also investigated. A design algorithm that summarises the different steps of the UIFO design is proposed. Then, the frequency procedure design is derived from time domain results by applying the factorisation approach, where we define some useful matrix fraction descriptions. Note that the order of this unknown input observers is equal to the dimension of the vector to be estimated. A numerical example is given to illustrate the effectiveness of the presented approach.

Recursive Determination of Parameter Uncertainty Intervals for Linear Models with Unknown But Bounded Errors

Abstract This paper proposes a new recursive method for determining parameter uncertainty intervals in the case of linear regression models with unknown but bounded errors. This method is based on the recursive construction of an orthotopic outer bounding approximation of the parameter membership set The orthotope center can be considered as the current estimate and the co-ordinates of the orthotope vertices directly provide the parameter uncertainty intervals. The proposed recursive estimation method is characterized by a small computational complexity. Simulation results are presented to illustrate the behavior of this method and to show its remarkable properties in terms of robustness with respect to measurement noise.

Identification of Non Linear Multivariable Processes Modelled on Reproducing Kernel Hilbert Space: Application to Tennessee Process

Abstract Abstract In this paper we extend the results obtained in Reproducing Kernel Hilbert Space (RKHS) modelling in the case of Single Input Single Output (SISO) processes to the multivariable (MIMO) ones. Once the model structure is established the model parameters are identified. The validation of the identified model is built on the Tennessee Eastman Process (TE) which is a highly non linear multivariable and non minimum phase chemical process. This process which is unstable in open loop is handled as closed loop controlled process

Nonlinear system modeling based on bilinear Laguerre orthonormal bases.

This paper proposes a new representation of discrete bilinear model by developing its coefficients associated to the input, to the output and to the crossed product on three independent Laguerre orthonormal bases. Compared to classical bilinear model, the resulting model entitled bilinear-Laguerre model ensures a significant parameter number reduction as well as simple recursive representation. However, such reduction still constrained by an optimal choice of Laguerre pole characterizing each basis. To do so, we develop a pole optimization algorithm which constitutes an extension of that proposed by Tanguy et al.. The bilinear-Laguerre model as well as the proposed pole optimization algorithm are illustrated and tested on a numerical simulations and validated on the Continuous Stirred Tank Reactor (CSTR) System.

Unknown Inputs Functional Observers Designs For Descriptor Systems with Constant Time Delay

Abstract In this paper, both time and frequency domain new designs of Unknown Inputs Functional Observers (UIFO) for a class of descriptor systems with a constant time delay are presented. The order of this unknown input observers is equal to the dimension of the vector to be estimated. The time procedure design is based on Lyapunov-Krasovskii stability theory where, after given the existence condition of such observers, the optimal gain implemented in the functional observer with internal delay design is obtained in terms of linear matrix inequalities (LMIs). A design algorithm of UIFO is proposed; The frequency procedure design is derived from time domain results by applying the factorization approach, where we define some useful Matrix Fraction Descriptions (MFDs). The effectiveness of the proposed approach is illustrated by a numerical example.

Online prediction model based on Reduced Kernel Principal Component Analysis

This paper proposes a new technique for online identification of a nonlinear system modeled on Reproducing Kernel Hilbert Space (RKHS) using kernel method. This new method uses the Reduced Kernel Principal Component Analysis (RKPCA) to update the principal component which represent the observations selected by the Kernel Principal Component Analysis method (KPCA). The KPCA is a nonlinear extension of Principal Component Analysis (PCA) to RKHS as it transforms the input data by a nonlinear mapping from the input space into a high dimensional feature space to which the PCA is performed. The proposed technique may be very helpful to design an adaptive control strategy of nonlinear systems.