Abdelkader Mbarek

Non-linear predictive controller for uncertain process modelled by GOBF-Volterra models

This paper proposes a new approach for synthesising a predictive control for non-linear uncertain process based on a proposed reduced complexity discrete-time Volterra model known as GOBF-Volterra model. This model, provided by expanding each Volterra kernel on independent generalised orthonormal basis functions (GOBF), is efficient for the synthesis of non-linear model-based predictive control (NMBPC) which copes with physical constraints and geometrical constraints due to parameter uncertainties. A quadratic criterion is optimised and a new optimisation algorithm, formulated as a quadratic programming (QP) under linear and non-linear constraints, is proposed. Simulation results on a chemical reactor are presented to illustrate the performance of the proposed NMBPC strategy for uncertain process. This reveals that the stability performance of the resulting closed-loop system depends on the choice of the tuning parameters.

Robust predictive control using Kautz model

This paper proposes a new approach for robust predictive control algorithm using development on the orthogonal Kautz function base. Bounding error identification techniques are used to update the uncertainty domain of the Kautz model coefficients which constraint the predictive control strategy.

Reduced complexity Volterra model of non-linear MISO system

In this paper, we propose a new dynamic non-linear MISO system model using discrete-time Volterra series. To provide a reduced complexity model, each Volterra kernel is expanded on independent generalised orthonormal bases (GOBs) associated to the inputs to develop a new black-box non-linear MISO-GOB-Volterra model. However, this reduction is ensured once the poles characterising each independent generalised orthonormal basis (GOB) are set to their optimal values. For the selection of optimal GOBs poles, we develop two new general approaches based on Gauss-Newton and exhaustive algorithms, the performances of which are illustrated and compared in simulation.

Optimal expansion of linear system using generalized orthogonal basis

This paper proposes a new method for determining the optimal pole of generalized orthonormal basis (GOB) which leads to an optimal system model developed on such basis. This optimal pole is obtained by solving a set of non linear equations. The proposed procedure is formulated for single-input/single-output (SISO) systems. The proposed algorithm is tested on simulations and good performances in term of approximation and calculus time are obtained.

Recursive updating of the exact non convex feasible parameter sets

The paper deals with the identification of bounded output error models. With this kind of model, the feasible parameter set is non convex and the classical bounded-error identification methods cannot be used to update such a set. The problem of updating a non convex feasible parameter set is addressed. That is achieved by decomposing the non convex set into convex subsets which can be updated using classical exact or outer bounding identification methods. An algorithm is proposed for carrying out such a decomposition and it is illustrated by means of simulation results.

Identification of nonlinear systems by the new representation ARX-Laguerre decoupled multimodel

This paper proposes a new alternative in the multimodel approach by expanding each ARX sub-model on independent orthonormal Laguerre bases by filtering the process input and output using Laguerre orthonormal functions. The resulting multimodel, entitled ARX-Laguerre decoupled multimodel, ensures the parameter number reduction with a recursive and easy representation. However, such reduction is 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. [17]. The ARX-Laguerre decoupled multimodel as well as the proposed pole optimization algorithm are illustrated and validated on a numerical simulation.

New algorithm for parallelotope updating in output error bounding

This paper proposes a new algorithm for updating an outer bounding parallelotope of the exact feasible parameter set when the model output error is unknown but bounded. The proposed method consists of a reformulation of the method proposed by A. Vicino and G. Zappa (IEEE Trans. Automatic Control, vol. 41, no. 6, pp. 774-784, 1996) for parallelotope updating when the model equation error is bounded, taking into account the constraints resulting from model output error bounding.

Non-linear system modelling based on NARX model expansion on Laguerre orthonormal bases

This study proposes a new representation of discrete Non-linear AutoRegressive with eXogenous inputs (NARX) model by developing its coefficients associated to the input, the output, the crossed product, the exogenous product and the autoregressive product on five independent Laguerre orthonormal bases. The resulting model, entitled NARX-Laguerre, ensures a significant parameter number reduction with respect to the NARX model. However, this reduction is still subject to an optimal choice of the Laguerre poles defining the five Laguerre bases. Therefore, the authors propose to use the genetic algorithm to optimise the NARX-Laguerre poles, based on the minimisation of the normalised mean square error. The performances of the resulting NARX-Laguerre model and the proposed optimisation algorithm are validated by numerical simulations and tested on the benchmark Continuous Stirred Tank Reactor.

Non linear predictive control algorithm based on Laguerre-Volterra models

This paper proposes a non linear predictive control algorithm based on Laguerre-Volterra model. This latter results from the expansion of discrete Volterra kernels on independent Laguerre basis. This expansion enables to alleviate the Volterra model complexity resulting from the high parameter number. As the yielded Laguerre-Volterra model is linear with respect to parameters, we develop a predictive control strategy using the classical technique that minimizes a quadratic criterion with respect to constraints due to sensors and actuators which are summarized by bounds on control, control increment and output signals.

Optimal expansion of discrete Volterra models using independent Laguerre basis

In this paper, the development of Volterra kernels on independent Laguerre basis is considered to provide Laguerre Volterra model. To minimise such model truncating order, the optimal Laguerre poles have to be identified. Two procedures based on gradient and Newton-Raphson methods are proposed. These methods are tested on simulation and the resulting poles converge to their optimal values. The yielded Laguerre-Volterra models are validated and their outputs fit the process one.