**Multimodel Control Design Using Unsupervised Classifiers**

**Nesrine ELFELLY ^{1,2}, Jean-Yves DIEULOT^{3}, Mohamed BENREJEB^{2}, Pierre BORNE^{1} **

^{1 }EC Lille, LAGIS, Cité Scientifique

59650Villeneuve d’Ascq, France,

nesrine.elfelly@ec-lille.fr

^{2 }ENI Tunis,UR LARA Automatique,

BP371002 Tunis LeBelvédère, Tunisia

dieulot@univ-lille1.fr

^{3 }Polytech Lille, LAGIS, Cité Scientifique,

59650Villeneuve d’Ascq, France,

**Abstract**: Multimodel approaches derive a smooth control law from the blending of local controllers using the concept of validities and domain overlapping. In this paper, it is demonstrated that unsupervised classification algorithms can be of a great help to design such parameters as the number of the models and their respective clusters, which will be performed using a respectively Rival Penalized Competitive Learning (RPCL) and simple or fuzzy K-means algorithms. The classical multimodel approach follows by deriving parametric model identification using the classification results for models orders and then parameters estimation. The determination of the global system control parameters results from a fusion of models control parameters. The case of a second order nonlinear system is studied to illustrate the efficiency of the proposed approach, and it is shown that this approach is much simpler that other multimodel control design methods which generally require a huge number of neighboring models.

**Keywords**: Complex systems, multimodel, identification, control, classification.

**CITE THIS PAPER AS**: Nesrine ELFELLY, Jean-Yves DIEULOT, Mohamed BENREJEB, Pierre BORNE, **Multimodel Control Design Using Unsupervised Classifiers**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 21 (1), pp. 101-108, 2012.

**1. Introduction **

The multimodel approach has arisen from the needs of process industries for which operations often include set-point changes and/or the co-existence of multiple operating modes. While nonlinear control is complicated to derive and tune, it is often more appropriate to consider a set of well-known operating points and their respective subsystems to achieve modelling or control by an accurate blending of the local systems/controllers. However, the multimodel approach owns, from its distributed structure, a high number of degrees of freedom, including the number and parameters of the different models representative of the system, the choice of the blending method and the design of a suitable control merging algorithm.

Over the last few years, many authors [e.g. 1,5] have proposed methods for identification and model structure validation, and a huge literature addresses linear models blending such as fuzzy Takagi-Sugeno models [e.g. 11]. However, the multimodel representation is more difficult to obtain when the subsystems are nonlinear and/or should be determined from raw input-output data. Some results were given in [7, 8]. In the main, classification of models with unsupervised algorithms was used to find an appropriate size for the model-base and estimate the models parameters, and the blending functions between several models were selected in the common case where the operating domains overlap.

Classification or neural techniques have been used for output to state modelling or control [1, 15, 19] and also to build multimodel representation and control from raw data; however, whereas Cho et al. [5] used Kohonen Self Organizing Map and K-means techniques [21], few other works have attempted to bridge the classification and multimodel control domains.

This paper thus proposes a practical approach for complex systems control based on classification algorithms while extending previous works in which the modelling issue was addressed [6, 8] and the preliminary results in [7]. Multimodel control is based on the multimodel representation and has been applied very successfully, for example, to chemical and biological plants (see e.g. [4, 18]). The procedure consists in designing a controller for each model of the base and to obtain a global control by some blending law. Local controls have been chosen as neural networks (e.g. [1]), PID (eg. [4]), predictive (e.g. [18]), or adaptive controllers [9], whereas the blending law can be selected either as a commutation between the partial controllers (e.g. [9]) or a fusion by using validity indexes [14]. However, again, these multimodel-based controllers suffer from the initial choice of model number and structure, when the operating points are not chosen a priori but should emerge from insight in input-output data.

In a first place, it will be recalled how to build a set ofmodels from input-output data using the fuzzy K-means algorithm and to determine the transition functions. An appropriate clustering method called Rival Penalized Competitive Learning (RPCL) [20] which is an extension of Kohonen competitive algorithm will enhance the determination of the number of models/clusters to be considered. Second, an adaptive – multimodel – controller will be obtained through a fusion of the parameters of the different controllers already designed for the models of the base by means of the appropriate validity indexes based on the residual approach [6, 8].

A nonlinear system which has been already presented in [5] allows confirming the relevance and the simplicity of the suggested approach, as results show that the number of local models can be reduced drastically.

**REFERENCES**:

- BARUCH, I. S., R. B. LOPEZ, J-L. OLIVARES, J-M. FLORES,
**A Fuzzy-neural Multi-model for Nonlinear Systems Identification and Control,**Fuzzy sets and systems, vol. 159, 2008, pp. 2650-2667. - BEN ABDENNOUR, R., P. BORNE, M. KSOURI, F. M’SAHLI,
**Identification et commande numérique des procédés industriels,**Editions Technip, Paris, France, 2001. - BEZDEK, J. C.,
**Pattern Recognition with Fuzzy Objective Function Algorithms**, Plenum Press, New York, 1981. - BÖLING, J. M., D. E. SEBORG, J. P. HESPANHA,
**Multi-model Adaptive Control of a Simulated pH Neutralization Process**, Control Engineering Practice, vol. 15, 2007, pp. 663-672. - CHO, J., J. C. PRINCIPE, D. ERDOGMUS, M. A. MOTTER,
**Quasi-sliding Mode Control Strategy based on Multiple-linear Models**, Neurocomputing, vol. 70, 2007, pp. 960-974. - ELFELLY, N., J.-Y. DIEULOT, P. BORNE,
**A Neural Approach of Multimodel Representation of Complex Processes,**International Journal of Computers, Communications & Control, vol. 3, 2008, pp. 149-160. - ELFELLY, N., J.-Y. DIEULOT, P. BORNE, M. BENREJEB,
**A Multimodel Approach of Complex Systems Identification and Control using Neural and Fuzzy Clustering Algorithms**, Proceeding of the 9th International Conference on Machine Learning and Applications, Washington (USA), 2010, pp. 93-98. - ELFELLY, N., J.-Y. DIEULOT, M. BENREJEB, P. BORNE,
**A New Approach for Multimodel Identification of Complex Systems based on Both Neural and Fuzzy Clustering Algorithms,**Engineering Applications of Artificial Intelligence, vol. 3, 2010, pp. 1064-1071. - FU, Y., CHAI, T.,
**Nonlinear Multivariable Adaptive Control using Multiple Models and Neural Networks**, Automatica, vol. 43, 2007, pp. 1101-1110. - GHARSALLAOUI, H., M. AYADI, M. BENREJEB, P. BORNE,
**Robust Flatness-based Multi-controllers Approach,**Studies in Informatics and Control, Vol. 19, No.4/2010, pp.357-358. - JAMEL, W., A. KHEDHER, N. BOUGUILA, K. BEN OTHMAN,
**State Estimation via Observers with Unknown Inputs: Application to a Particular Class of Uncertain T-S Systems,**Studies in Informatics and Control, vol.19, No. 3/2010, pp. 219-228. - M. KSOURI-LAHMARI, P. BORNE, M. BENREJEB,
**Multimodel: the Construction of Model Bases**, Studies in Informatics and Control, Vol. 13, No.3/2004, pp. 199-210. - LORIMIER, L., P. BORNE,
**Local Observer-based Multi-control and Online Validity Estimation for Multiple-model Control of Complex Systems**, IEEE International Conference Systems, Man, and Cybernetics, vol. 1, 2003, pp. 822-827. - MANIOUDAKIS, G. D., E. N. DEMIRIS, S. D. LIKOTHANASSIS,
**A Self-organized Neural Network based on the Multi-model Partitioning Theory**, Neurocomputing, vol. 37, 2001, pp. 1-29. - MURLIDHARAN NAIR, T., C. L. ZHENG, J. LYNN FINK, R. O. STUART, M. GRIBSKOV,
**Rival Penalized Competitive Learning (RPCL): A Topology-determining Algorithm for Analyzing Gene Expression Data**, Computational Biology and Chemistry, 27, 2003, pp. 565-574. - NASCIMENTO, S., B. MIRKIN, F. MOURA-PIRES,
**A Fuzzy Clustering Model of Data and Fuzzy C-means**, The Ninth IEEE International Conference on Fuzzy Systems, vol. 1, 2000, pp. 302-307. - ÖZKAN, L., M. V. KOTHARE, C. GEORGAKIS,
**Control of a Solution Copolymerization Reactor using Multi-model Predictive Control**, Chemical Engineering Science, vol. 58, 2003, pp. 1207-1221. - PATIC, P. C., R. M. ZEMOURI, L. DUTA,
**Recurrent Neural Networks in Linear Systems Controlling**, Studies in Informatics and Control, vol. 19, No. 2/2010, pp. 153-158. - TAMBE, S. S., B. D. KULKARNI, P. B. DESHPANDE,
**Elements of Artificial Neural Networks with Selected Applications on Chemical Engineering, and Chemical & Biological Sciences**, Simulations & Advanced Controls, Louisville-KY, USA, 1996. - XUE, Z. K., S. Y. LI,
**Multi-model Modelling and Predictive Control based on Local Model Networks,**Control and Intelligent Systems, 34, 2006, pp. 105-112.