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Adaptive Finite-Time Stabilization of Chaotic Flow with a Single Unstable Node Using a Nonlinear Function-Based Global Sliding Mode

  • Saleh MobayenEmail author
  • Jun Ma
  • Gisela Pujol-Vazquez
  • Leonardo Acho
  • Quanmin Zhu
Research paper

Abstract

This article presents a novel adaptive finite-time stabilization technique based on global sliding mode for disturbed chaotic flow with a single unstable node. The considered chaotic flow has unusual characteristics containing attractor merging, symmetry breaking, attracting tori and different forms of multi-stability. A nonlinear function is employed in the global sliding surface to modify damping ratio and improve the transient performance. The damping ratio of the closed-loop system is improved when the states converge to the origin. Using the new chattering-free controller, the reaching mode is removed and the sliding behavior is presented right from the first instant. The adaptive finite-time tuning law eliminates the requirement of the information about the disturbances’ bounds. Illustrative simulations are provided to display the efficiency of the proposed scheme.

Keywords

Global sliding mode Adaptive gain tuning Finite-time control Chaotic flow Unstable node 

Notes

Acknowledgements

This work was partially supported by the Spanish Ministry of Economy, Industry and Competitiveness, under Grants DPI2016-77407-P (AEI/FEDER, UE) and DPI2015-64170-R (MINECO/FEDER).

References

  1. Bai J, Lu SQ, Liu J (2014) Study and application of sliding mode control strategy for high-power current source inverter. Appl Mech Mater 527:259–266CrossRefGoogle Scholar
  2. Barambones O, Alkorta P (2011) A robust vector control for induction motor drives with an adaptive sliding-mode control law. J Frankl Inst 348(2):300–314CrossRefGoogle Scholar
  3. Chen C-K, Yan J-J, Liao T-L (2007) Sliding mode control for synchronization of Rössler systems with time delays and its application to secure communication. Phys Scr 76(5):436CrossRefGoogle Scholar
  4. Chen F, Jiang R, Wen C, Su R (2015) Self-repairing control of a helicopter with input time delay via adaptive global sliding mode control and quantum logic. Inf Sci 316:123–131CrossRefGoogle Scholar
  5. Chu Y, Fei J (2015) Adaptive global sliding mode control for MEMS gyroscope using RBF neural network. Math Probl Eng 2015:9 pages, Article ID 403180MathSciNetzbMATHGoogle Scholar
  6. Chu Y, Fang Y, Fei J (2017) Adaptive neural dynamic global PID sliding mode control for MEMS gyroscope. Int J Mach Learn Cybern 8(5):1707–1718CrossRefGoogle Scholar
  7. Cid-Pastor A, Martinez-Salamero L, El Aroudi A, Giral R, Calvente J, Leyva R (2013) Synthesis of loss-free resistors based on sliding-mode control and its applications in power processing. Control Eng Pract 21(5):689–699CrossRefGoogle Scholar
  8. González I, Salazar S, Lozano R (2014) Chattering-free sliding mode altitude control for a quad-rotor aircraft: real-time application. J Intell Rob Syst 73(1–4):137–155CrossRefGoogle Scholar
  9. Jeong S, Chwa D (2018) Coupled multiple sliding-mode control for robust trajectory tracking of hovercraft with external disturbances. IEEE Trans Ind Electron 65(5):4103–4113CrossRefGoogle Scholar
  10. Jiang B, Gao C, Xie J (2015) Passivity based sliding mode control of uncertain singular Markovian jump systems with time-varying delay and nonlinear perturbations. Appl Math Comput 271:187–200MathSciNetGoogle Scholar
  11. Kengne J, Njitacke Tabekoueng Z, Kamdoum Tamba V, Nguomkam Negou A (2015) Periodicity, chaos, and multiple attractors in a memristor-based Shinriki’s circuit. Chaos Interdiscip J Nonlinear Sci 25(10):103126MathSciNetCrossRefGoogle Scholar
  12. Li S-B, Li K-Q, Wang J-Q, Yang B (2010) Nonsingular fast terminal-sliding-mode control method and its application on vehicular following system. Control Theory Appl 5:004Google Scholar
  13. Li H, Yu J, Hilton C, Liu H (2013) Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T–S fuzzy approach. IEEE Trans Ind Electron 60(8):3328–3338CrossRefGoogle Scholar
  14. Li X-B, Ma L, Ding S-H (2015) A new second-order sliding mode control and its application to inverted pendulum. Acta Automatica Sinica 1:022Google Scholar
  15. Li P, Ma J, Zheng Z (2016) Robust adaptive sliding mode control for uncertain nonlinear MIMO system with guaranteed steady state tracking error bounds. J Frankl Inst 353(2):303–321MathSciNetCrossRefGoogle Scholar
  16. Lv M, Wang C, Ren G, Ma J, Song X (2016) Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn 85(3):1479–1490CrossRefGoogle Scholar
  17. Majd VJ, Mobayen S (2015) An ISM-based CNF tracking controller design for uncertain MIMO linear systems with multiple time-delays and external disturbances. Nonlinear Dyn 80(1–2):591–613MathSciNetCrossRefGoogle Scholar
  18. Martinez-Guerra R, Yu W (2008) Chaotic synchronization and secure communication via sliding-mode observer. Int J Bifurc Chaos 18(01):235–243MathSciNetCrossRefGoogle Scholar
  19. Mobayen S (2015) An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems. Nonlinear Dyn 82(1–2):599–610MathSciNetCrossRefGoogle Scholar
  20. Mobayen S (2016) A novel global sliding mode control based on exponential reaching law for a class of underactuated systems with external disturbances. J Comput Nonlinear Dyn 11(2):021011CrossRefGoogle Scholar
  21. Mobayen S, Baleanu D (2017) Linear matrix inequalities design approach for robust stabilization of uncertain nonlinear systems with perturbation based on optimally-tuned global sliding mode control. J Vib Control 23(8):1285–1295MathSciNetCrossRefGoogle Scholar
  22. Mobayen S, Baleanu D, Tchier F (2016) Second-order fast terminal sliding mode control design based on LMI for a class of non-linear uncertain systems and its application to chaotic systems. J Vib Control 23(18):2912–2925MathSciNetCrossRefGoogle Scholar
  23. Mobayen S, Tchier F, Ragoub L (2017) Design of an adaptive tracker for n-link rigid robotic manipulators based on super-twisting global nonlinear sliding mode control. Int J Syst Sci 48(9):1990–2002MathSciNetCrossRefGoogle Scholar
  24. Nasiri A, Nguang SK, Swain A (2014) Adaptive sliding mode control for a class of MIMO nonlinear systems with uncertainties. J Frankl Inst 351(4):2048–2061MathSciNetCrossRefGoogle Scholar
  25. Ni J, Liu L, Liu C, Hu X, Li S (2017) Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Express Briefs 64(2):151–155CrossRefGoogle Scholar
  26. Polyakov A, Fridman L (2014) Stability notions and Lyapunov functions for sliding mode control systems. J Frankl Inst 351(4):1831–1865MathSciNetCrossRefGoogle Scholar
  27. Qin H, Ma J, Jin W, Wang C (2014) Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci China Technol Sci 57(5):936–946CrossRefGoogle Scholar
  28. Sangpet T, Kuntanapreeda S (2010) Output feedback control of unified chaotic systems based on feedback passivity. Int J Bifurc Chaos 20(05):1519–1525CrossRefGoogle Scholar
  29. Sprott J, Jafari S, Pham V-T, Hosseini ZS (2015) A chaotic system with a single unstable node. Phys Lett A 379(36):2030–2036MathSciNetCrossRefGoogle Scholar
  30. Tsai C-H, Chung H-Y, Yu F-M (2004) Neuro-sliding mode control with its applications to seesaw systems. IEEE Trans Neural Netw 15(1):124–134CrossRefGoogle Scholar
  31. Van M, Kang H-J, Shin K-S (2014) Backstepping quasi-continuous high-order sliding mode control for a Takagi–Sugeno fuzzy system with an application for a two-link robot control. Proc Inst Mech Eng Part C J Mech Eng Sci 228(9):1488–1500CrossRefGoogle Scholar
  32. Wang B, Shi P, Karimi HR (2014) Fuzzy sliding mode control design for a class of disturbed systems. J Frankl Inst 351(7):3593–3609MathSciNetCrossRefGoogle Scholar
  33. Wei Z, Moroz I, Sprott J, Akgul A, Zhang W (2017) Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo. Chaos Interdiscip J Nonlinear Sci 27(3):033101MathSciNetCrossRefGoogle Scholar
  34. Wu M, Chen J (2014) A discrete-time global quasi-sliding mode control scheme with bounded external disturbance rejection. Asian J Control 16(6):1839–1848MathSciNetCrossRefGoogle Scholar
  35. Wu L, Mazumder SK, Kaynak O (2018) Sliding mode control and observation for complex industrial systems—part II. IEEE Trans Ind Electron 65(1):830–833CrossRefGoogle Scholar
  36. Xiu C, Hou J, Xu G, Zang Y (2017) Improved fast global sliding mode control based on the exponential reaching law. Adv Mech Eng.  https://doi.org/10.1177/1687814016687967 CrossRefGoogle Scholar
  37. Xu Y, Zhou W, Fang JA, Xie C, Tong D (2016) Finite-time synchronization of the complex dynamical network with non-derivative and derivative coupling. Neurocomputing 173:1356–1361CrossRefGoogle Scholar
  38. Xu Y, Meng D, Xie C, You G, Zhou W (2018a) A class of fast fixed-time synchronization control for the delayed neural network. J Frankl Inst 355(1):164–176MathSciNetCrossRefGoogle Scholar
  39. Xu Y, Ke Z, Xie C, Zhou W (2018b) Dynamic evolution analysis of stock price fluctuation and its control. Complexity 2018:9 pages, Article ID 5728090Google Scholar
  40. Yang J, Li S, Yu X (2013) Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. IEEE Trans Ind Electron 60(1):160–169CrossRefGoogle Scholar
  41. Yuan F, Wang G, Wang X (2016) Extreme multistability in a memristor-based multi-scroll hyper-chaotic system. Chaos Interdiscip J Nonlinear Sci 26(7):073107MathSciNetCrossRefGoogle Scholar
  42. Zhang X, Liu X, Zhu Q (2014) Adaptive chatter free sliding mode control for a class of uncertain chaotic systems. Appl Math Comput 232:431–435MathSciNetzbMATHGoogle Scholar
  43. Zhao X, Yang H, Zong G (2017) Adaptive neural hierarchical sliding mode control of nonstrict-feedback nonlinear systems and an application to electronic circuits. IEEE Trans Syst Man Cybern Syst 47(7):1394–1404CrossRefGoogle Scholar
  44. Zhong T, Yuanwei J, Chengyin Y, Nan J (2014) Global sliding mode control based on observer for TCP network. In: The 26th chinese control and decision conference (2014 CCDC) 2014, p 4946–4950Google Scholar

Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Faculty of EngineeringUniversity of ZanjanZanjanIran
  2. 2.Department of PhysicsLanzhou University of TechnologyLanzhouChina
  3. 3.Department of MathematicsUniversitat Politècnica de Catalunya-BarcelonaTech (ESEIAAT)TerrasaSpain
  4. 4.Department of MathematicsUniversitat Politècnica de Catalunya-BarcelonaTech (EEBE)BarcelonaSpain
  5. 5.Department of Engineering Design and MathematicsUniversity of the West of EnglandBristolUK

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