Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

Nonlinear Dynamics

Volumn 80, Issue 1-2, 2015, Pages 249-267

  Balasubramaniam, P ^a   Muthukumar, P ^a   Ratnavelu, K ^b  

^a GANDHIGRAM RURAL UNIVERSITY   (India)

^b UNIVERSITY OF MALAYA   (Malaysia)

Author keywords

Chaos; Fractional order system; Fuzzy logic; Sliding mode control; Synchronization

Indexed keywords

CHAOS THEORY; CHAOTIC SYSTEMS; CRYPTOGRAPHY; FUZZY LOGIC; SYNCHRONIZATION;

FRACTIONAL INTEGRALS; FRACTIONAL ORDER; FRACTIONAL-ORDER CHAOTIC SYSTEMS; FRACTIONAL-ORDER DYNAMICAL SYSTEMS; FRACTIONAL-ORDER SYSTEMS; IMAGE ENCRYPTION AND DECRYPTION; INTEGER ORDER;

SLIDING MODE CONTROL;

EID: 84925519785     PISSN: 0924090X     EISSN: 1573269X     Source Type: Journal    
DOI: 10.1007/s11071-014-1865-4     Document Type: Article

References (46)

1. Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge (2003)
2. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)
3. Abdullah, A.: Synchronization and secure communication of uncertain chaotic systems based on full-order and reduced-order output-affine observers. Appl. Math. Comput. 219, 10000–10011 (2013)
4. Wu, X., Wang, H., Lu, H.: Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication. Nonlinear Anal. Real World Appl. 13, 1441–1450 (2012)
5. Sheu, L.J.: A speech encryption using fractional chaotic systems. Nonlinear Dyn. 65, 103–108 (2011)
6. Muthukumar, P., Balasubramaniam, P.: Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography. Nonlinear Dyn. 74, 1169–1181 (2013)
7. Muthukumar, P., Balasubramaniam, P., Ratnavelu, K.: Synchronization of a novel fractional order stretch-twist-fold (STF) flow chaotic system and its application to a new authenticated encryption scheme (AES). Nonlinear Dyn. 77, 1547–1559 (2014)
8. Muthukumar, P., Balasubramaniam, P., Ratnavelu, K.: Synchronization and an application of a novel fractional order King Cobra chaotic system. Chaos 24, 033105 (2014)
9. Wang, B., Jian, J., Yu, H.: Adaptive synchronization of fractional-order memristor-based Chua’s system. Syst. Sci. Control Eng. 2, 291–296 (2014)
10. Zhang, L., Yan, Y.: Robust synchronization of two different uncertain fractional-order chaotic systems via adaptive sliding mode control. Nonlinear Dyn. 76, 1761–1767 (2014)
11. Wang, X., Zhang, X., Ma, C.: Modified projective synchronization of fractional-order chaotic systems via active sliding mode control. Nonlinear Dyn. 69, 511–517 (2012)
12. Matouk, A.E., Elsadany, A.A.: Achieving synchronization between the fractional-order hyperchaotic Novel and Chen systems via a new nonlinear control technique. Appl. Math. Lett. 29, 30–35 (2014)
13. Xu, Y., He, Z.: Synchronization of variable-order fractional financial system via active control method. Cent. Eur. J. Phys. 11, 824–835 (2013)
14. Jin-Gui, L.: A novel study on the impulsive synchronization of fractional-order chaotic systems. Chin. Phys. B 22, 060510 (2013)
15. Odibat, Z.: A note on phase synchronization in coupled chaotic fractional order systems. Nonlinear Anal. Real World Appl. 13, 779–789 (2012)
16. Silva, M.F., Machado, J.A.T., Lopes, A.M.: Fractional order control of a hexapod robot. Nonlinear Dyn. 38, 417–433 (2004)
17. Silva, M.F., Machado, J.A.T.: Fractional order PD$$^{\alpha }$$α joint control of legged robots. J. Vib. Control 12, 1483–1501 (2006)
18. Delavari, H., Lanusse, P., Sabatier, J.: Fractional order controller design for a flexible link manipulator robot. Asian J. Control 15, 783–795 (2013)
19. Monje, C.A., Ramos, F., Feliu, V., Vinagre, B.M.: Tip position control of a lightweight flexible manipulator using a fractional order controller. IET Control Theory Appl. 1, 1451–1460 (2007)
20. Li, Y., Xu, Q.: Adaptive sliding mode control with perturbation estimation and PID sliding surface for motion tracking of a piezo-driven micromanipulator. IEEE Trans. Control Syst. Technol. 18, 798–810 (2010)
21. Shi, P., Xia, Y., Liu, G.P., Rees, D.: On designing of sliding-mode control for stochastic jump systems. IEEE Trans. Autom. Control 51, 97–103 (2006)
22. Yue, M., Wei, X., Li, Z.: Adaptive sliding-mode control for two-wheeled inverted pendulum vehicle based on zero-dynamics theory. Nonlinear Dyn. 76, 459–471 (2014)
23. Utkin, V.I.: Sliding mode control design principles and applications to electric drives. IEEE Trans. Ind. Electron. 40, 23–36 (1993)
24. Shtessel, Y.B., Shkolnikov, I.A., Brown, M.D.: An asymptotic second-order smooth sliding mode control. Asian J. Control 5, 498–504 (2003)
25. Balochian, S.: Sliding mode control of fractional order nonlinear differential inclusion systems. Evolv. Syst. 4, 145–152 (2013)
26. Xu, H., Mirmirani, M.D., Ioannou, P.A.: Adaptive sliding mode control design for a hypersonic flight vehicle. J. Guid. Control Dyn. 27, 829–838 (2004)
27. Plestan, F., Shtessel, Y., Bregeault, V., Poznyak, A.: New methodologies for adaptive sliding mode control. Int. J. Control 83, 1907–1919 (2010)
28. Aghababa, M.P.: Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems. Int. J. Control 86, 1744–1756 (2013)
29. Li, C., Su, K., Wu, L.: Adaptive sliding mode control for synchronization of a fractional-order chaotic system. J. Comput. Nonlinear Dyn. 8, 031005 (2013)
30. Gao, Z., Liao, X.: Integral sliding mode control for fractional-order systems with mismatched uncertainties. Nonlinear Dyn. 72, 27–35 (2013)
31. Palm, R.: Sliding mode fuzzy control. In: Proceedings of IEEE Conference on Fuzzy Systems, pp. 519–526, San Diego (1992)
32. Delavari, H., Ghaderi, R., Ranjbar, A., Momani, S.: Fuzzy fractional order sliding mode controller for nonlinear systems. Commun. Nonlinear Sci. Numer. Simul. 15, 963–978 (2010)
33. Lin, T.C., Lee, T.Y., Balas, V.E.: Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems. Chaos Solitons Fract. 44, 791–801 (2011)
34. Chen, D., Zhang, R., Sprott, J.C., Ma, X.: Synchronization between integer-order chaotic systems and a class of fractional-order chaotic system based on fuzzy sliding mode control. Nonlinear Dyn. 70, 1549–1561 (2012)
35. Faieghi, M.R., Delavari, H., Baleanu, D.: Control of an uncertain fractional-order Liu system via fuzzy fractional-order sliding mode control. J. Vib. Control 18, 1366–1374 (2012)
36. Li-Ming, W., Yong-Guang, T., Yong-Quan, C., Feng, W.: Generalized projective synchronization of the fractional-order chaotic system using adaptive fuzzy sliding mode control. Chin. Phys. B 23, 100501 (2014)
37. Arshad, S., Lupulescu, V.: Fractional differential equation with the fuzzy initial condition. Electron. J. Differ. Equ. 2011, 1–8 (2011)
38. Agarwal, R.P., Arshad, S., O’Regan, D., Lupulescu, V.: Fuzzy fractional integral equations under compactness type condition. Fract. Calc. Appl. Anal. 15, 572–590 (2012)
39. Allahviranloo, T., Armand, A., Gouyandeh, Z., Ghadiri, H.: Existence and uniqueness of solutions for fuzzy fractional Volterra–Fredholm integro-differential equations. J. Fuzzy Set Valued Anal. 2013, 1–9 (2013)
40. Takači, D., Takači, A., Takači, A.: On the operational solutions of fuzzy fractional differential equations. Fract. Calc. Appl. Anal. 17, 1100–1113 (2014)
41. Caputo, M.: Linear models of dissipation whose $$Q$$Q is almost frequency independent—II. Geophys. J. R. Astron. Soc. 13, 529–539 (1967)
42. Matignon, D.: Stability results for fractional differential equations with applications to control processing. In: Proceedings of Computational Engineering in Systems Applications vol. 2, pp. 963–968, Lille, France (1996)
43. Xing-yuan, W., Yi-jie, H., Ming-jun, W.: Chaos control of a fractional order modified coupled dynamos system. Nonlinear Anal. 71, 6126–6134 (2009)
44. Zhen, W., Xia, H., Yu-Xia, L., Xiao-Na, S.: A new image encryption algorithm based on the fractional-order hyperchaotic Lorenz system. Chin. Phys. B 22, 010504 (2013)
45. Xu, Y., Wang, H., Li, Y., Pei, B.: Image encryption based on synchronization of fractional chaotic systems. Commun. Nonlinear Sci. Numer. Simul. 19, 3735–3744 (2014)
46. Liu, H., Wang, X., Kadir, A.: Color image encryption using Choquet fuzzy integral and hyper chaotic system. Optik 124, 3527–3533 (2013)