A novel robust discrete-time integral sliding mode tracking control design for time-varying delay MIMO systems with unknown uncertainties.

This paper proposes a novel robust tracking control scheme for discrete time linear uncertain Multiple-Input Multiple-Output (MIMO) systems subject to time-varying delay on the states. The considered system is affected by unknown but norm bounded uncertainties on parameters as well as matched disturbances on the states. The designed controller is based upon a proposed novel integral sliding surface and a new switching type of reaching law. Sufficient conditions based on Linear Matrix Inequalities (LMIs) and a suitable Lyapunov-Krasovskii Functional (LKF) are derived in order to guarantee the asymptotic stability of such system. The proposed controller ensures a good tracking performance despite the presence of the time varying delay and the matched/unmatched disturbances. Moreover and thanks to the proposed integral surface, the time reaching phase is eliminated and the chattering phenomenon is significantly reduced. The proposed controller is applied on an Autonomous Underwater Vehicle (AUV) to follow a prescribed desired trajectory. The simulation results illustrate the effectiveness of such controller.

Robust adaptive sliding mode control for uncertain systems with unknown time-varying delay input.

This article focuses on robust adaptive sliding mode control law for uncertain discrete systems with unknown time-varying delay input, where the uncertainty is assumed unknown. The main results of this paper are divided into three phases. In the first phase, we propose a new sliding surface is derived within the Linear Matrix Inequalities (LMIs). In the second phase, using the new sliding surface, the novel Robust Sliding Mode Control (RSMC) is proposed where the upper bound of uncertainty is supposed known. Finally, the novel approach of Robust Adaptive Sliding ModeControl (RASMC) has been defined for this type of systems, where the upper limit of uncertainty which is assumed unknown. In this new approach, we have estimate the upper limit of uncertainties and we have determined the control law based on a sliding surface that will converge to zero. This novel control laws are been validated in simulation on an uncertain numerical system with good results and comparative study. This efficiency is emphasized through the application of the new controls on the two physical systems which are the process trainer PT326 and hydraulic system two tanks.

New methods of Laguerre pole optimization for the ARX model expansion on Laguerre bases.

The ARX-Laguerre model is a very important reduced complexity representation of linear system. However a significant reduction of this model is subject to an optimal choice of both Laguerre poles. Therefore we propose in this paper two new methods to estimate, from input/output measurements, the optimal values of Laguerre poles of the ARX-Laguerre model. The first method is based on the Newton-Raphson's iterative technique where we prove that the gradient and the Hessian can be expressed analytically. The second method is based on Genetic Algorithms. Both proposed algorithms are tested on a numerical example and on a heating benchmark.

Moving window KPCA with reduced complexity for nonlinear dynamic process monitoring.

This paper proposes an improved Reduced Kernel Principal Component Analysis (RKPCA) for handling nonlinear dynamic systems. The proposed method is entitled Moving Window Reduced Kernel Principal Component Analysis (MW-RKPCA). It consists firstly in approximating the principal components (PCs) of the KPCA model by a reduced data set that approaches "properly" the system behavior in the order to elaborate an RKPCA model. Secondly, the proposed MW-RKPCA consists on updating the RKPCA model using a moving window. The relevance of the proposed MW-RKPCA technique is illustrated on a Tennessee Eastman process.

Dimensionality reduction of RKHS model parameters.

This paper proposes a new method to reduce the parameter number of models developed in the Reproducing Kernel Hilbert Space (RKHS). In fact, this number is equal to the number of observations used in the learning phase which is assumed to be high. The proposed method entitled Reduced Kernel Partial Least Square (RKPLS) consists on approximating the retained latent components determined using the Kernel Partial Least Square (KPLS) method by their closest observation vectors. The paper proposes the design and the comparative study of the proposed RKPLS method and the Support Vector Machines on Regression (SVR) technique. The proposed method is applied to identify a nonlinear Process Trainer PT326 which is a physical process available in our laboratory. Moreover as a thermal process with large time response may help record easily effective observations which contribute to model identification. Compared to the SVR technique, the results from the proposed RKPLS method are satisfactory.

Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model.

In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS).

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.

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.

Decomposition of an ARX model on Laguerre orthonormal bases.

In this paper, we propose a new reduced complexity model by expanding a discrete-time ARX model on Laguerre orthonormal bases. To ensure an efficient complexity reduction, the coefficients associated to the input and the output of the ARX model are expanded on independent Laguerre bases, to develop a new black-box linear ARX-Laguerre model with filters on model input and output. The parametric complexity reduction with respect to the classical ARX model is proved theoretically. The structure and parameter identification of the ARX-Laguerre model is achieved by a new proposed approach which consists in solving an optimization problem built from the ARX model without using system input/output observations. The performances of the resulting ARX-Laguerre model and the proposed identification approach are illustrated by numerical simulations and validated on benchmark manufactured by Feedback known as Process Trainer PT326. A possible extension of the proposed model to a multivariable process is formulated.