ARX model decomposed on Meixner-Like orthonormal bases.

The present study provides a new modeling of linear slowly starting systems. More precisely, this new approach extends the technique of filtering only the input using Meixner-Like (M-L) filters to filter both the output and input of the system outlined by an ARX model. Therefore, the idea is to develop the input and output parameters of ARX modeling over 2 M-L bases. So as to ensure an optimal representation, the two M-L poles are optimized using Newton-Raphson (N-R) and Genetic Algorithms (GA) methods. A new method is proposed for Model Predictive Control (MPC) using the obtained optimal model that is called ARXMeixner-Like (ARXM-L). A numerical example of system having delay and three examples of experimental research: A supersonic jet engine inlet, a Process Trainer PT326 and a Quanser aero experiment with one degree of freedom attitude control are made.

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.

Adaptive MPC based on MIMO ARX-Laguerre model.

This paper proposes a method for synthesizing an adaptive predictive controller using a reduced complexity model. This latter is given by the projection of the ARX model on Laguerre bases. The resulting model is entitled MIMO ARX-Laguerre and it is characterized by an easy recursive representation. The adaptive predictive control law is computed based on multi-step-ahead finite-element predictors, identified directly from experimental input/output data. The model is tuned in each iteration by an online identification algorithms of both model parameters and Laguerre poles. The proposed approach avoids time consuming numerical optimization algorithms associated with most common linear predictive control strategies, which makes it suitable for real-time implementation. The method is used to synthesize and test in numerical simulations adaptive predictive controllers for the CSTR process benchmark.

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.

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.