Sliding mode control design for synchronization of fractional order chaotic systems and its application to a new cryptosystem

International Journal of Dynamics and Control

Volumn 5, Issue 1, 2017, Pages 115-123

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

^a GANDHIGRAM RURAL UNIVERSITY   (India)

^b UNIVERSITY OF MALAYA   (Malaysia)

Author keywords

Chaos; Cryptography; Fractional order system; Sliding mode control; Synchronization

Indexed keywords

CHAOS THEORY; CHAOTIC SYSTEMS; CRYPTOGRAPHY; SYNCHRONIZATION;

FRACTIONAL ORDER; FRACTIONAL-ORDER CHAOTIC SYSTEMS; FRACTIONAL-ORDER SYSTEMS; IMAGE ENCRYPTION AND DECRYPTION; ITS APPLICATIONS; SLIDING MODE CONTROL DESIGN; SYNCHRONIZATION METHOD;

SLIDING MODE CONTROL;

EID: 85013777098     PISSN: 2195268X     EISSN: 21952698     Source Type: Journal    
DOI: 10.1007/s40435-015-0169-y     Document Type: Article

References (39)

1. Grigorenko I, Grigorenko E (2003) Chaotic dynamics of the fractional Lorenz system. Phys Rev Lett 91:034101
2. Li C, Chen G (2004) Chaos in the fractional order Chen system and its control. Chaos Solitons Fractals 22:549–554
3. Sheu LJ, Chen HK, Chen JH, Tam LM, Chen WC, Lin KT, Kang Y (2008) Chaos in the Newton–Leipnik system with fractional order. Chaos Solitons Fractals 36:98–103
4. Wang XY, Wang MJ (2007) Dynamic analysis of the fractional-order Liu system and its synchronization. Chaos 17:033106
5. Petras I (2009) Chaos in the fractional-order Volta’s system: modeling and simulation. Nonlinear Dyn 57:157–170
6. Li C, Chen G (2004) Chaos and hyperchaos in the fractional-order Rössler equations. Phys A 341:55–61
7. Lu JG (2005) Chaotic dynamics and synchronization of fractional-order Arneodo’s systems. Chaos Solitons Fractals 26:1125–1133
8. Muthukumar P, Balasubramaniam P (2013) Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography. Nonlinear Dyn 74:1169–1181
9. Zhang R, Gong J (2014) Synchronization of the fractional-order chaotic system via adaptive observer. Syst Sci Control Eng 2:751–754
10. Matouk AE, Elsadany AA (2014) Achieving synchronization between the fractional-order hyperchaotic Novel and Chen systems via a new nonlinear control technique. Appl Math Lett 29:30–35
11. Kuntanapreeda S (2012) Robust synchronization of fractional-order unified chaotic systems via linear control. Comput Math Appl 63:183–190
12. Zhang L, Yan Y (2014) Robust synchronization of two different uncertain fractional-order chaotic systems via adaptive sliding mode control. Nonliner Dyn 76:1761–1767
13. Wang B, Jian J, Yu H (2014) Adaptive synchronization of fractional-order memristor-based Chua’s system. Syst Sci Control Eng 2:291–296
14. Radwan AG, Moaddy K, Salama KN, Momani S, Hashim I (2014) Control and switching synchronization of fractional order chaotic systems using active control technique. J Adv Res 5:125–132
15. Matouk AE (2011) Chaos, feedback control and synchronization of a fractional-order modified autonomous Van der Pol-Duffing circuit. Commun Nonlinear Sci Numer Simulat 16:975–986
16. Islam M, Islam B, Islam N (2014) Chaos control in Shimizu Morioka system by Lie algebraic exact linearization. Int J Dyn Control 2:386–394
17. Ojo KS, Njah AN, Olusola OI (2014) Generalized compound synchronization of chaos in different orders chaotic Josephson junctions. Int J Dynam Control. doi:10.1007/s40435-014-0122-5
18. Wang X, Zhang X, Ma C (2012) Modified projective synchronization of fractional-order chaotic systems via active sliding mode control. Nonlinear Dyn 69:511–517
19. Chen DY, Liu YX, Ma XY, Zhang RF (2012) Control of a class of fractional-order chaotic systems via sliding mode. Nonlinear Dyn 67:893–901
20. Razminia A, Baleanu D (2013) Complete synchronization of commensurate fractional order chaotic systems using sliding mode control. Mechatronics 23:873–879
21. Balasubramaniam P, Muthukumar P, Ratnavelu K (2015) Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system. Nonlinear Dyn 80:249–267
22. Yin M, Wang LW (2008) A new study in encryption based on fractional order chaotic system. J Electron Sci Technol 6:302–305
23. Liang H, Wang Z, Yue Z, Lu R (2012) Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication. Kybernetika 48:190–205
24. Wu X, Wang H, Lu H (2012) 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
25. Zhen W, Xia H, Yu-Xia L, Xiao-Na S (2013) A new image encryption algorithm based on the fractional-order hyperchaotic Lorenz system. Chin Phys B 22:010504
26. Xu Y, Wang H, Li Y, Pei B (2014) Image encryption based on synchronization of fractional chaotic systems. Commun Nonlinear Sci Numer Simul 19:3735–3744
27. Muthukumar P, Balasubramaniam P, Ratnavelu K (2014) Synchronization and an application of a novel fractional order King Cobra chaotic system. Chaos 24:033105
28. Muthukumar P, Balasubramaniam P, Ratnavelu K (2014) 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
29. Caputo M (1967) Linear models of dissipation whose Q is almost frequency independent-II. Geophys J Int 13:529–539
30. Wang Z, Sun Y (2014) Analysis of a fractional order nonlinear system based on the frequency domain approximation. Int J Eng Pract Res 3:74–77
31. Charef A, Sun HH, Tsao YY, Onaral B (1992) Fractal system as represented by sigularity function. IEEE Trans Autom Control 37:1465–1470
32. Tavazoei MS, Haeri M (2007) Unreliability of frequency-domain approximation in recognising chaos in fractional-order systems. IET Signal Process 1:171–181
33. Tavazoei MS, Haeri M (2008) Limitations of frequency domain approximation for detecting chaos in fractional order systems. Nonlinear Anal 69:1299–1320
34. Hartly TT, Lorenzo CF, Qammer HK (1995) Chaos in a fractional order Chua’s system. IEEE Trans Circuits Syst I 42:485–490
35. Matignon D (1996) Stability results for fractional differential equations with applications to control processing. In: Computational engineering in systems applications. France, vol 2, pp 963–968
36. Travazoei MS, Haeri M (2007) A necessary condition for double scroll attractor existence in fractional-order systems. Phys Lett A 367:102–113
37. Pehlivan I, Wei Z (2012) Analysis, nonlinear control, and chaos generator circuit of another strange chaotic system. Turk J Electr Eng Comput Sci 20:1229–1239
38. Balasubramaniam P, Muthukumar P (2014) Synchronization of chaotic systems using feedback controller: an application to Diffie–Hellman key exchange protocol and ElGamal public key cryptosystem. J Egypt Math Soc 22:365–372
39. Parvin Z, Seyedarabi H, Shamsi M (2014) A new secure and sensitive image encryption scheme based on new substitution with chaotic function. Multimed Tools Appl. doi:10.1007/s11042-014-2115-y