# GENETIC AND ELLIPSOID ALGORITHMS FOR NONLINEAR PREDICTIVE CONTROL

### Kaouther Laabidi, Faouzi Bouani, Mekki Ksouri

#### 2005

#### Abstract

This paper deals with the constrained predictive control of nonlinear systems. Artificial Neural Networks (ANN) are used as a process model. The control law is derived by minimizing a non convex criterion. The optimization problem is solved using Ellipsoid and genetic algorithms. The structure and operators of the combining two algorithms have been specifically developed for control design problem. Simulation results are presented to illustrate the performances of the proposed predictive controller.

#### References

- Boyd S., El Ghaoui L., Feron E. and Balakrishnan V. “Linear Matrix Inqualities in System and Control Theory”, edition SIAM 1994
- Clarke D. W., C. Mohtadi and P. S. Tuffs, “Generalized predictive Control”. Part I and II, Automatica, Vol. 23, No. 23, pp.137-160, 1987.
- Goldberg D. E., "Genetic Algorithms in search, optimization and machine learning", Addison-Wesley, Massachusetts, 1991.
- Hunt K. J., D. Sbarbaro, R. Zbikowski and P. J. Gawthrop, "Neural networks for control systems - a survey", Automatica, Vol. 28, No. 6, pp. 1083-1112, 1992.
- Levin A. U. and K. S. Narendra, "Control of nonlinear dynamical systems using neural networks”. Part II: Observability, identification, and control, IEEE Trans. Neural Networks, Vol. 7, No. 1, pp. 30-42, 1996.
- Najim K., A. Rusnak, A. Meszaros and M. Fikar "Constrained long-range predictive control based on artificial neural networks", International Journal of System Sciences, Vol. 28, No. 12, pp. 1211-1226, 1997.
- Narendra K. S. and K. Parthasarathy, "Identification and control of dynamical systems using neural networks", IEEE Trans. Neural Networks, Vol. 1, No. 1, pp. 4-27, 1990.
- Primoz P. and G. Igor, “Non linear model predictive control of a cutting process” Neurocomputing, Vol. 43, pp. 107-126, 2002.
- Saldanha R. R., R. H. C. Takahashi, J. A. Vasconcelos and J. A. Ramirez, "Adaptive Deep-Cut Method in Ellipsoidal Optimization for Electromagnetic Design", IEEE Transactions on Magnetics, vol. 35, No. 3, pp. 1746-1749,1999.
- Takahashi R. H. C., R. R. Saldanha, W. Dias-Filho and J. A. Ramirez, "A New Constrained Ellipsoidal Algorithm for Nonlinear Optimization With Equality Constraints", IEEE Transactions on Magnetics, Vol. 39, No. 3, pp. 1289-1292, 2003.

#### Paper Citation

#### in Harvard Style

Laabidi K., Bouani F. and Ksouri M. (2005). **GENETIC AND ELLIPSOID ALGORITHMS FOR NONLINEAR PREDICTIVE CONTROL** . In *Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 972-8865-29-5, pages 288-291. DOI: 10.5220/0001181302880291

#### in Bibtex Style

@conference{icinco05,

author={Kaouther Laabidi and Faouzi Bouani and Mekki Ksouri},

title={GENETIC AND ELLIPSOID ALGORITHMS FOR NONLINEAR PREDICTIVE CONTROL},

booktitle={Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2005},

pages={288-291},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001181302880291},

isbn={972-8865-29-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - GENETIC AND ELLIPSOID ALGORITHMS FOR NONLINEAR PREDICTIVE CONTROL

SN - 972-8865-29-5

AU - Laabidi K.

AU - Bouani F.

AU - Ksouri M.

PY - 2005

SP - 288

EP - 291

DO - 10.5220/0001181302880291