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

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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.

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References

  • Bai J, Lu SQ, Liu J (2014) Study and application of sliding mode control strategy for high-power current source inverter. Appl Mech Mater 527:259–266

    Article  Google Scholar 

  • 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):300–314

    Article  MATH  Google Scholar 

  • 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):436

    Article  MATH  Google Scholar 

  • 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 316:123–131

    Article  MATH  Google Scholar 

  • 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 403180

  • 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):1707–1718

    Article  Google Scholar 

  • 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):689–699

    Article  Google Scholar 

  • 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):137–155

    Article  Google Scholar 

  • 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):4103–4113

    Article  Google Scholar 

  • 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 271:187–200

    MathSciNet  MATH  Google Scholar 

  • 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):103126

    Article  MathSciNet  MATH  Google Scholar 

  • 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 5:004

    Google Scholar 

  • 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):3328–3338

    Article  Google Scholar 

  • 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 1:022

    Google Scholar 

  • 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):303–321

    Article  MathSciNet  MATH  Google Scholar 

  • 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):1479–1490

    Article  Google Scholar 

  • 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):591–613

    Article  MathSciNet  MATH  Google Scholar 

  • Martinez-Guerra R, Yu W (2008) Chaotic synchronization and secure communication via sliding-mode observer. Int J Bifurc Chaos 18(01):235–243

    Article  MathSciNet  MATH  Google Scholar 

  • 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):599–610

    Article  MathSciNet  MATH  Google Scholar 

  • 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):021011

    Article  Google Scholar 

  • 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):1285–1295

    Article  MathSciNet  MATH  Google Scholar 

  • 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):2912–2925

    Article  MathSciNet  MATH  Google Scholar 

  • 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):1990–2002

    Article  MathSciNet  MATH  Google Scholar 

  • 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):2048–2061

    Article  MathSciNet  MATH  Google Scholar 

  • 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):151–155

    Article  Google Scholar 

  • Polyakov A, Fridman L (2014) Stability notions and Lyapunov functions for sliding mode control systems. J Frankl Inst 351(4):1831–1865

    Article  MathSciNet  MATH  Google Scholar 

  • 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):936–946

    Article  Google Scholar 

  • Sangpet T, Kuntanapreeda S (2010) Output feedback control of unified chaotic systems based on feedback passivity. Int J Bifurc Chaos 20(05):1519–1525

    Article  MATH  Google Scholar 

  • Sprott J, Jafari S, Pham V-T, Hosseini ZS (2015) A chaotic system with a single unstable node. Phys Lett A 379(36):2030–2036

    Article  MathSciNet  MATH  Google Scholar 

  • 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):124–134

    Article  Google Scholar 

  • 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):1488–1500

    Article  Google Scholar 

  • Wang B, Shi P, Karimi HR (2014) Fuzzy sliding mode control design for a class of disturbed systems. J Frankl Inst 351(7):3593–3609

    Article  MathSciNet  MATH  Google Scholar 

  • 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):033101

    Article  MathSciNet  MATH  Google Scholar 

  • Wu M, Chen J (2014) A discrete-time global quasi-sliding mode control scheme with bounded external disturbance rejection. Asian J Control 16(6):1839–1848

    Article  MathSciNet  MATH  Google Scholar 

  • Wu L, Mazumder SK, Kaynak O (2018) Sliding mode control and observation for complex industrial systems—part II. IEEE Trans Ind Electron 65(1):830–833

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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 173:1356–1361

    Article  Google Scholar 

  • 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):164–176

    Article  MathSciNet  MATH  Google Scholar 

  • 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 5728090

  • 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):160–169

    Article  Google Scholar 

  • 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):073107

    Article  MathSciNet  Google Scholar 

  • Zhang X, Liu X, Zhu Q (2014) Adaptive chatter free sliding mode control for a class of uncertain chaotic systems. Appl Math Comput 232:431–435

    MathSciNet  MATH  Google Scholar 

  • 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):1394–1404

    Article  Google Scholar 

  • 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 4946–4950

Download references

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).

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Authors and Affiliations

  1. Department of Electrical Engineering, Faculty of Engineering, University of Zanjan, Zanjan, Iran

    Saleh Mobayen

  2. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Jun Ma

  3. Department of Mathematics, Universitat Politècnica de Catalunya-BarcelonaTech (ESEIAAT), Terrasa, Spain

    Gisela Pujol-Vazquez

  4. Department of Mathematics, Universitat Politècnica de Catalunya-BarcelonaTech (EEBE), Barcelona, Spain

    Leonardo Acho

  5. Department of Engineering Design and Mathematics, University of the West of England, Bristol, UK

    Quanmin Zhu

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  1. Saleh Mobayen
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  2. Jun Ma
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  3. Gisela Pujol-Vazquez
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  4. Leonardo Acho
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  5. Quanmin Zhu
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Correspondence to Saleh Mobayen.

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Mobayen, S., Ma, J., Pujol-Vazquez, G. et al. Adaptive Finite-Time Stabilization of Chaotic Flow with a Single Unstable Node Using a Nonlinear Function-Based Global Sliding Mode. Iran J Sci Technol Trans Electr Eng 43 (Suppl 1), 339–347 (2019). https://doi.org/10.1007/s40998-018-0153-6

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