# Neural network-based MRAC control of dynamic nonlinear systems

Ghania Debbache; Abdelhak Bennia; Noureddine Golea

International Journal of Applied Mathematics and Computer Science (2006)

- Volume: 16, Issue: 2, page 219-232
- ISSN: 1641-876X

## Access Full Article

top## Abstract

top## How to cite

topDebbache, Ghania, Bennia, Abdelhak, and Golea, Noureddine. "Neural network-based MRAC control of dynamic nonlinear systems." International Journal of Applied Mathematics and Computer Science 16.2 (2006): 219-232. <http://eudml.org/doc/207787>.

@article{Debbache2006,

abstract = {This paper presents direct model reference adaptive control for a class of nonlinear systems with unknown nonlinearities. The model following conditions are assured by using adaptive neural networks as the nonlinear state feedback controller. Both full state information and observer-based schemes are investigated. All the signals in the closed loop are guaranteed to be bounded and the system state is proven to converge to a small neighborhood of the reference model state. It is also shown that stability conditions can be formulated as linear matrix inequalities (LMI) that can be solved using efficient software algorithms. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation results are presented to show the effectiveness of the approach.},

author = {Debbache, Ghania, Bennia, Abdelhak, Golea, Noureddine},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {LMI; neural networks; reference model; observer; adaptivecontrol; stability; nonlinear systems; adaptive control},

language = {eng},

number = {2},

pages = {219-232},

title = {Neural network-based MRAC control of dynamic nonlinear systems},

url = {http://eudml.org/doc/207787},

volume = {16},

year = {2006},

}

TY - JOUR

AU - Debbache, Ghania

AU - Bennia, Abdelhak

AU - Golea, Noureddine

TI - Neural network-based MRAC control of dynamic nonlinear systems

JO - International Journal of Applied Mathematics and Computer Science

PY - 2006

VL - 16

IS - 2

SP - 219

EP - 232

AB - This paper presents direct model reference adaptive control for a class of nonlinear systems with unknown nonlinearities. The model following conditions are assured by using adaptive neural networks as the nonlinear state feedback controller. Both full state information and observer-based schemes are investigated. All the signals in the closed loop are guaranteed to be bounded and the system state is proven to converge to a small neighborhood of the reference model state. It is also shown that stability conditions can be formulated as linear matrix inequalities (LMI) that can be solved using efficient software algorithms. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation results are presented to show the effectiveness of the approach.

LA - eng

KW - LMI; neural networks; reference model; observer; adaptivecontrol; stability; nonlinear systems; adaptive control

UR - http://eudml.org/doc/207787

ER -

## References

top- Billings S.A., Jamaluddin H.B. and Chen S. (1992): Properties of neurali networks with applications to modeling nonlinear dynamical systems. - Int. J. Contr., Vol. 55, No. 1, pp. 193-224. Zbl0742.93001
- Cybenko G. (1989): Approximations by superpositions of a sigmoidal function. - Math. Signals Syst., Vol. 2, pp. 303-314. Zbl0679.94019
- Cotter M.E. (1990): The Stone-Weierstrass theorem and its applications to neural nets. - IEEE Trans. Neural Netw., Vol. 1, No. 4, pp. 290-295.
- Chang Y-C. and Yen H-M. (2005): Adaptive output feedback tracking control for a class of uncertain nonlinear systems using neural networks. - IEEE Trans. Syst. Man Cybern., Part B, Vol. 35, No. 6, pp. 1311-1316.
- Ferrari S. and Stengel R.F. (2005): Smooth function approximation using neural networks. - IEEE Trans. Neural Netw., Vol. 16, No. 1, pp. 24-38.
- Ge S.S., Hang C.C. and Zhang T. (1999): A direct method for robust adaptive nonlinear control with guaranteed transient performance. - Syst. Contr. Lett., Vol. 37, pp. 275-284. Zbl0948.93032
- Huang S.N., Tan K.K. and Lee T.H. (2006): Nonlinear adaptive control of interconnected systems using neural networks. - IEEE Trans. Neural Netw., Vol. 17, No. 1, pp. 243-246.
- Landau Y.D. (1979): Adaptive Control: The Model Reference Approach. - New York: Marcel Dekker. Zbl0475.93002
- Narendra K.S. and Parthasarathy K. (1990): Identification and control of dynamical systems using neural networks. - IEEE Trans. Neural Netw., Vol. 1,No. 1, pp. 4-27.
- Neidhoefer J.C., Cox C.J. and Saeks R.E. (2003): Development and application of a Lyapunov synthesis based neural adaptive controller. - IEEE Trans. Syst. Man Cybern., Vol. 33, No. 1, pp. 125-137.
- Park J. and Sandberg I.W. (1991): Universal approximation using radial basis function networks. - Neural Comput., Vol. 3, No. 2, pp. 246-257.
- Poznyak A.S., You W., Sanchez E.E. and Perez J.P. (1999): Nonlinear adaptive trajectory tracking using dynamic neural networks. - IEEE Trans. Neural Netw., Vol. 10, No. 6, pp. 1402-1411.
- Patino H.D. and Liu D. (2000): Neural network-based model reference adaptive control system. - IEEE Trans. Syst. Man Cybern., Vol. 30, No. 1,pp. 198-204.
- Plett G.L. (2003): Adaptive inverse control of linear and nonlinear systems using dynamic neural networks. - IEEE Trans. Neural Netw., Vol. 14, No. 2, pp. 360-376.
- Rivals I. and Personnaz L. (2000): Nonlinear internal model control using neural networks: Application to processes with delay and design issues. - IEEE Trans. Neural Netw., Vol. 11, No. 1, pp. 80-90.
- Sastry S. and Bodson M. (1989): Adaptive Control: Stability, Convergence and Robustness. - Upper Saddle River, NJ: Prentice-Hall. Zbl0721.93046
- Sanner R.M. and Slotine J.E. (1992): Gaussian networks for direct adaptive control. - IEEE Trans. Neural Netw., Vol. 3, No. 6, pp. 837-863.
- Spooner J.T. and Passino K.M. (1996): Stable adaptive control using fuzzy systems and neural networks. - IEEE Trans. Neural Netw., Vol. 4,No. 3, pp. 339-359.
- Seshagiri S. and Khalil H. (2000): Output feedback control of nonlinearsystems using RBF neural networks. - IEEE Trans. Neural Netw., Vol. 11,No. 1, pp. 69-79.
- Yesildirek A. and Lewis F.L. (1995): Feedback linearization using neural networks. - Automatica, Vol. 31, No. 11, pp. 1659-1664. Zbl0847.93032
- Yu S.-H. and Annaswamy A.M. (1997): Adaptive control of nonlinear dynamic systems using adaptive neural networks. - Automatica, Vol. 33, No. 11, pp. 1975-1995. Zbl0913.93041
- Zhihong M., Wu H.R. and Palaniswami M. (1998): An adaptive tracking controller using neural networks for a class of nonlinear systems. - IEEE Trans. Neural Netw., Vol. 9, No. 5, pp. 947-955.
- Zhang Y., Peng P.Y. and Jiang Z.P. (2000): Stable neural controller design for unknown nonlinear systems using back stepping. - IEEE Trans. Neural Netw., Vol. 11, No. 6, pp. 1347-1359.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.