Hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems

• Autorzy: Serrano F. , Rossell J. M.

Identyfikatory

DOI

10.1515/ama-2017-0015

• Języki publikacji: EN

Abstrakty

EN

In this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyperchaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropria.

Słowa kluczowe

EN

chaos synchronization; passive control; type-2 fuzzy controller; chaotic system

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2017
• Tom: Vol. 11, no. 2
• Strony: 96--103
• Opis fizyczny: Bibliogr. 30 poz., rys., tab., wykr.

Twórcy

autor

Serrano F.

• Central American Technical University (UNITEC), Tegucigalpa, Zona Jacaleapa, Honduras

autor

Rossell J. M.

• Department of Mathematics, Universitat Politècnica de Catalunya (UPC), Av. Bases de Manresa, 61-73 08242-Manresa, Spain

Bibliografia

• 1. Castillo O., Melin P. (2008), Type-2 Fuzzy Logic: Theory and Applications, Springer Verlag, Germany.
• 2. Castillo O., Melin P. (2014), A review on interval type-2 fuzzy logic applications in intelligent control, Inf. Sciences, 279, 615-631.
• 3. Castillo O., Rico, D. (2006), Intelligent control of dynamic systems using type-2 fuzzy logic and stasbility issues, International Mathematical Forum, 1(28), 1371-1382.
• 4. Chen Z.-M., Djidjeli K., Price W. (2006), Computing Lyapunov exponents based on the solution expression of the variational system, Applied Mathematics and Computation, 174(2), 982- 996.
• 5. Dadras S., Momeni H. (2013), Passivity-based fractional-order integral sliding-mode control design for uncertain fractional order nonlinear systems, Mechatronics, 23(7), 880-887.
• 6. Dieci L., Vleck E.S.V. (1995), Computation of a few Lyapunov exponents for continuous and discrete dynamical systems, Applied Numerical Mathematics, 17(3), 275-291.
• 7. Effati S., Saberi-Nadjafi J., Saberi Nik H. (2014), Optimal and adaptive control for a kind of 3D chaotic and 4D hyper- chaotic systems, Applied Mathematical Modelling, 38(2), 759-774.
• 8. Fayek H., Elamvazuthi I., Perumal N., Venkatesh B. (2014), A controller based on optimal type-2 fuzzy logic: Systematic design, optimization and real-time implementation, ISA Transactions, 53(5),1583-1591.
• 9. Haddad W.M., Chellaboina V. (2008), Nonlinear dynamical systems and control a Lyapunov-based approach, Princeton University Press, New Jersey, USA.
• 10. Hagras, H. (2004). A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots. Fuzzy Systems, IEEE Transactions on, Vol. 12, No. 4, 524-539.
• 11. He D., Xu J., Chen Y., Tan, N. (1999). A simple method for the computation of the conditional Lyapunov exponents, Communications in Nonlinear Science and Numerical Simulation, 4(2), 113-117.
• 12. Kang H., Vachtsevanos G. (1992), Adaptive fuzzy logic control, Fuzzy Systems, IEEE International Conference, 407-414.
• 13. Karnik N., Mendel J., Liang Q. (1999), Type-2 fuzzy logic systems, Fuzzy Systems, IEEE Transactions, 7(6), 643-658.
• 14. Liu S., Sun J., Geng Z. (2013), Passivity-based finite-time attitude control problem, Control Conference (ASCC), 1-6.
• 15. Martino F., Sessa S. (2014), Type-2 interval fuzzy rule based systems in spatial analysis, Information Sciences, 279, 199-212.
• 16. Mendel J. (2005), On a 50 percent savings in the computation of the centroid of a symmetrical interval type-2 fuzzy set, Information Sciences, 172(3-4), 417-430.
• 17. Mendel J. (2007a), Advances in type-2 fuzzy sets and systems, Information Sciences, 177(1), 84-110.
• 18. Mendel J. (2007b), Type-2 fuzzy sets and systems: An overview, Computational Intelligence Magazine, IEEE, 2(1), 20-29.
• 19. Mendel J., Wu H. (2007), New results about the centroid of an interval type-2 fuzzy set, including the centroid of a fuzzy granule, Information Sciences, 177(2), 360-377.
• 20. Morales-Mata I., Tang Y., Lopez M., Santillan S. (2008), A design procedure of fuzzy PD control for mechanical systems, Control and Decision Conference, China, 5325-5330.
• 21. Ontanon-Garcia L., Campos-Canton E. (2013, Preservation of a two-wing Lorenz-like attractor with stable equilibria, Journal of the Franklin Institute, 350(10), 2867-2880.
• 22. Protasov V., Jungers R. (2013), Lower and upper bounds for the largest Lyapunov exponent of matrices, Linear Algebra and its Applications, 438 (11), 4448- 4468.
• 23. Richter H. (2003), Controlling chaos in maps with multiple strange attractors, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 13(10), 3037-3051.
• 24. Singh M., Gupta J. (2007), A new algorithm basetype-2 fuzzy controller for diabetic patient, Int. J. Biomedical Engineering and Technology, 1(1), 19-40.
• 25. Turksen I. (1999), Type I and type II fuzzy system modeling, Fuzzy Sets and Systems, 106(1), 11-34.
• 26. Wang Y.-F., Yu Z.-G. (2011), A type-2 fuzzy method for identification of disease-related genes on microarrays, International Journal of Bioscience, Biochemistry and Bioinformatics, 1(1), 73-78.
• 27. Yonemoto K., Yanagawa T. (2007), Estimating the Lyapunov exponent from chaotic time series with dynamic noise, Statistical Methodology, 4(4), 461-480.
• 28. Zhou P., Huang K. (2014), A new 4-D non-equilibrium fractionalorder chaotic system and its circuit implementation, Communications in Nonlinear Science and Numerical Simulation, 19(6), 2005-2011.
• 29. Zhou S.-M., Garibaldi J., John R., Chiclana F. (2009), On constructing parsimonious type-2 fuzzy logic systems via influential rule selection, Fuzzy Systems, IEEE Transactions, 17(3), 654–667.
• 30. Zhu B., Huo W. (2013), Passivity-based adaptive trajectory linearization control for a model-scaled unmanned helicopter, Control Conference (CCC), Chinese, 2879-2884.

Uwagi

This work was partially supported by the Spanish Ministry of Economy and Competitiveness under Grant DPI2015-64170-R/FEDER

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).