Fuzzy Logic Control System Stability Analysis Based on Lyapunov’s Direct Method

Authors

  • Radu-Emil Precup "Politehnica" University of Timi¸soara Department of Automation and Applied Informatics
  • Marius-Lucian Tomescu "Aurel Vlaicu" University of Arad Computer Science Faculty Complex Universitar M, Str. Elena Dragoi 2, RO-310330 Arad, Romania
  • Ștefan Preitl "Politehnica" University of Timi¸soara Department of Automation and Applied Informatics Bd. V. Parvan 2, RO-300223 Timi¸soara, Romania

Keywords:

fuzzy logic controller, LaSalle’s invariance principle, Lyapunov function candidate

Abstract

A stability analysis method for nonlinear processes controlled by Takagi- Sugeno (T-S) fuzzy logic controllers (FLCs) is proposed. The stability analysis of these fuzzy logic control systems is done in terms of Lyapunov’s direct method. The stability theorem presented here ensures sufficient conditions for the stability of the fuzzy logic control systems. The theorem enables the formulation of a new stability analysis algorithm that offers sufficient stability conditions for nonlinear processes controlled by a class of T-S FLCs. In addition, the paper includes an illustrative example that describes one application of this algorithm in the design of a stable fuzzy logic control system.

References

M. M. Bălaș, V. E. Bălaș¸s, World Knowledge for Control Applications by Fuzzy-Interpolative Systems, International Journal of Computers, Communications & Control, Vol. III, Suppl. Issue: Proceedings of ICCCC 2008, pp. 28-32, 2008.

A. Bazoula, M.S. Djouadi, H. Maaref, Formation Control of Multi-Robots via Fuzzy Logic Technique, International Journal of Computers, Communications & Control, Vol. III, Suppl. Issue: Proceedings of ICCCC 2008, pp. 179-184. 2008.

D. Bellomo, D. Naso, and R. Babuška, Adaptive fuzzy control of a non-linear servo-drive: theory and experimental results, Engineering Applications of Artificial Intelligence, Vol. 21, Issue 6, pp. 846-857, 2008. http://dx.doi.org/10.1016/j.engappai.2007.11.002

S. Blažic and I. Škrjanc, Design and stability analysis of fuzzy model-based predictive control - a case study, Journal of Intelligent and Robotic Systems, Vol. 49, Issue 3, pp. 279-292, 2007. http://dx.doi.org/10.1007/s10846-007-9147-8

S. Ertugrul, Predictive modeling of human operators using parametric and neuro-fuzzy models by means of computer-based identification experiment, Engineering Applications of Artificial Intelligence Vol. 21, Issue 2, pp. 259-268, 2008. http://dx.doi.org/10.1016/j.engappai.2007.03.007

G. Feng, A survey on analysis and design of model-based fuzzy control systems, IEEE Transactions on Fuzzy Systems, Vol. 14, Issue 5, pp. 676-697, 2006. http://dx.doi.org/10.1109/TFUZZ.2006.883415

D. Hladek, J. Vascak, and P. Sincak, Multi-robot control system for pursuit-evasion problem, Journal of Electrical Engineering, Vol. 60, Issue 3, pp. 143-148, 2009.

L. Horváth and I. J. Rudas, Towards content oriented integration of product and robot system models, International Symposium on Logistics and Industrial Informatics, Wildau, pp. 7-12, 2007. http://dx.doi.org/10.1109/LINDI.2007.4343503

G.-H. Hwang, D.-W. Kim, J.-H. Lee, and Y.-J. An, Design of fuzzy power system stabilizer using adaptive evolutionary algorithm, Engineering Applications of Artificial Intelligence, Vol. 21, Issue 1, pp. 86-96, 2008. http://dx.doi.org/10.1016/j.engappai.2006.11.008

Z. C. Johanyák and S. Kovács: Sparse fuzzy system generation by rule base extension, 11th IEEE International Conference of Intelligent Engineering Systems, Budapest, pp. 99-104, 2007. http://dx.doi.org/10.1109/ines.2007.4283680

H. K. Khalil, Nonlinear Systems, Third Edition, Prentice Hall, Englewood Cliffs, NJ, 2002.

K. Michels, F. Klawonn, R. Kruse, and A. Nürnberger, Fuzzy Control: Fundamentals, Stability and Design of Fuzzy Controllers, Springer Verlag, Berlin, Heidelberg, New York, 2006.

B. M. Mohan and A. Sinha, Analytical structure and stability analysis of a fuzzy PID controller, Applied Soft Computing, Vol. 8, Issue 1, pp. 749-758, 2008. http://dx.doi.org/10.1016/j.asoc.2007.06.003

A. G. Perry, G. Feng, Y.-F. Liu, and P. C. Sen, A design method for PI-like fuzzy logic controllers for DC-DC converter, IEEE Transactions on Industrial Electronics, Vol. 54, Issue 5, pp. 2688-2696, 2007. http://dx.doi.org/10.1109/TIE.2007.899858

R.-E. Precup, S. Preitl, and G. Faur, PI predictive fuzzy controllers for electrical drive speed control: methods and software for stable development, Computers in Industry, Vol. 52, Issue 3, pp. 253-270, 2003. http://dx.doi.org/10.1016/S0166-3615(03)00130-1

R.-E. Precup, S. Preitl, I. J. Rudas, M. L. Tomescu, and J. K. Tar, Design and experiments for a class of fuzzy controlled servo systems, IEEE/ASME Transactions on Mechatronics, Vol. 13, Issue 1, pp. 22-35, 2008. http://dx.doi.org/10.1109/TMECH.2008.915816

E. Tian and C. Peng, Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay, Fuzzy Sets and Systems, Vol. 157, Issue 4, pp. 544-559, 2006. http://dx.doi.org/10.1016/j.fss.2005.06.022

T. Vesselenyi, S. Dzi¸tac, I. Dzi¸tac and M.-J. Manolescu, Fuzzy and Neural Controllers for a Pneumatic Actuator, International Journal of Computers, Communications & Control, Vol. II, No. 4, pp. 375-387, 2007. http://dx.doi.org/10.15837/ijccc.2007.4.2368

K.W.Wong, D. Tikk, T. D. Gedeon, and L. T. Kóczy, Fuzzy rule interpolation for multidimensional input spaces with applications: a case study, IEEE Transactions on Fuzzy Systems, Vol. 13, Issue 6, pp. 809-819, 2005. http://dx.doi.org/10.1109/TFUZZ.2005.859316

J. Yoneyama, Robust stability and stabilization for uncertain Takagi-Sugeno fuzzy time-delay systems, Fuzzy Sets and Systems, Vol. 158, Issue 2, pp. 115-134, 2007. http://dx.doi.org/10.1016/j.fss.2006.09.004

Published

2009-12-01

Issue

Vol. 4 No. 4 (2009): International Journal of Computers Communications & Control (December)

Section

Articles

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