Lorenz System Stabilization Using Fuzzy Controllers

Radu-Emil Precup, Marius L. Tomescu, Stefan Preitl

Abstract


The paper suggests a Takagi Sugeno (TS) fuzzy logic controller (FLC) designed to stabilize the Lorentz chaotic systems. The stability analysis of the fuzzy control system is performed using Barbashin-Krasovskii theorem. This paper proves that if the derivative of Lyapunov function is negative semi-definite for each fuzzy rule then the controlled Lorentz system is asymptotically stable in the sense of Lyapunov. The stability theorem suggested here offers sufficient conditions for the stability of the Lorenz system controlled by TS FLCs. An illustrative example describes the application of the new stability analysis method.

Keywords


chaotic systems, fuzzy control, Lyapunov functions, nonlinear equations and systems

Full Text:

PDF

References


Calvo O., Cartwright J. H. E., Fuzzy control of chaos, International Journal of Bifurcation and Chaos, Vol. 8, Number 8, pp. 1743-1747, 1998.
http://dx.doi.org/10.1142/S0218127498001443

Khalil H. K., Nonlinear Systems, 3rd Edition, Prentice Hall, Englewood Cliffs, NJ, 2002.

Lima R., Pettini M., Suppression of chaos by resonant parametric perturbations, Physical Letter A, Vol. 41, pp. 726-733, 1990.
http://dx.doi.org/10.1103/physreva.41.726

Lorenz E. N., The Essence of Chaos, University of Washington Press, 1993.
http://dx.doi.org/10.4324/9780203214589

Ott E., Grebogi, C., Yorke, J. A, Controlling chaos, Physical Review Letter, Vol. 64, pp. 1196-1199, 1990.
http://dx.doi.org/10.1103/PhysRevLett.64.1196

Precup R.-E., Preitl S., Optimisation criteria in development of fuzzy controllers with dynamics, Engineering Applications of Artificial Intelligence, Vol. 17, No. 6, pp. 661-674, 2004.
http://dx.doi.org/10.1016/j.engappai.2004.08.004

Pyragas K, Continuous control of chaos by self-controlling feedback, Physical Letter A, Vol. 170, pp. 421-427, 1992.
http://dx.doi.org/10.1016/0375-9601(92)90745-8

Pyragas K., Tamaevièius A., Experimental control of chaos by delayed self-controlling feedback, Physical Letter A, Vol. 180, pp. 99-102, 1993.
http://dx.doi.org/10.1016/0375-9601(93)90501-P

Schuster H. G., Handbook of Chaos Control: Foundations and Applications, Wiley-VCH Verlag GmbH, 1999.
http://dx.doi.org/10.1002/3527607455

Wang H. O., Tanaka K., Fuzzy Modeling and Control of Chaotic Systems, in Integration of Fuzzy Logic and Chaos Theory, Springer-Verlag, Berlin, Heidelberg, 2006.
http://dx.doi.org/10.1007/3-540-32502-6_3

Zhong L., Halang W. A., Chen, G. (Eds.), Integration of Fuzzy Logic and Chaos Theory, Springer- Verlag, Berlin, Heidelberg, 2006.




DOI: https://doi.org/10.15837/ijccc.2007.3.2360



Copyright (c) 2017 Radu-Emil Precup, Marius L. Tomescu, Stefan Preitl

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC-BY-NC  License for Website User

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]


INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2018: IF=1.585..

IJCCC is indexed in Scopus from 2008 (CiteScore2018 = 1.56):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.

 

 Impact Factor in JCR2018 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.585 (Q3). Scopus: CiteScore2018=1.56 (Q2);

SCImago Journal & Country Rank

Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.