Adaptive synchronization control based on QPSO algorithm with interval estimation for fractional-order chaotic systems and its application in secret communication

In this paper, the synchronization problem and its application in secret communication are investigated for two fractional-order chaotic systems with unequal orders, different structures, parameter uncertainty and bounded external disturbance. On the basis of matrix theory, properties of fractional calculus and adaptive control theory, we design a feedback controller for realizing the synchronization. In addition, in order to make it better apply to secret communication, we design an optimal controller based on optimal control theory. In the meantime, we propose an improved quantum particle swarm optimization (QPSO) algorithm by introducing an interval estimation mechanism into QPSO algorithm. Further, we make use of QPSO algorithm with interval estimation to optimize the proposed controller according to some performance indicator. Finally, by comparison, numerical simulations show that the controller not only can achieve the synchronization and secret communization well, but also can estimate the unknown parameters of the systems and bounds of external disturbance, which verify the effectiveness and applicability of the proposed control scheme.

[1]  Mohammad Pourmahmood Aghababa,et al.  Design of hierarchical terminal sliding mode control scheme for fractional-order systems , 2015 .

[2]  Hooman Fatoorehchi,et al.  Feedback control strategies for a cerium-catalyzed Belousov–Zhabotinsky chemical reaction system , 2015 .

[3]  I Podlubny.  Fractional-order systems and (PID mu)-D-lambda-controllers , 1999 .

[4]  Pagavathigounder Balasubramaniam,et al.  Synchronization of a novel fractional order stretch-twist-fold (STF) flow chaotic system and its application to a new authenticated encryption scheme (AES) , 2014, Nonlinear Dynamics.

[5]  Zhang Ruo-Xun,et al.  Synchronization of fractional-order chaotic systems with different structures , 2008 .

[6]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[7]  Tong Zhang,et al.  Robust output feedback control for fractional order nonlinear systems with time-varying delays , 2016, IEEE/CAA Journal of Automatica Sinica.

[8]  I. Podlubny.  Fractional differential equations , 1998 .

[9]  Long Zhou,et al.  Chaos Multiscale-Synchronization between Two Different fractional-Order hyperchaotic Systems Based on Feedback Control , 2013, Int. J. Bifurc. Chaos.

[10]  Yan Shi,et al.  Disturbance-Observer-Based Robust Synchronization Control for a Class of Fractional-Order Chaotic Systems , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Young-Hun Lim,et al.  Stability and Stabilization of Fractional-Order Linear Systems Subject to Input Saturation , 2013, IEEE Transactions on Automatic Control.

[12]  Donglian Qi,et al.  Synchronization for fractional order chaotic systems with uncertain parameters , 2016 .

[13]  G. Adomian.  A review of the decomposition method and some recent results for nonlinear equations , 1990 .

[14]  Jun-Guo Lu,et al.  Stability Analysis of a Class of Nonlinear Fractional-Order Systems , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[15]  Hua Wang,et al.  Image encryption based on synchronization of fractional chaotic systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[16]  Ping Zhou,et al.  A practical synchronization approach for fractional-order chaotic systems , 2017 .

[17]  Kehui Sun,et al.  Chaos synchronization between two different fractional-order hyperchaotic systems , 2011 .

[18]  Ruoxun Zhang,et al.  Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach , 2013 .

[19]  Zaid Odibat,et al.  A note on phase synchronization in coupled chaotic fractional order systems , 2012 .

[20]  Xia Huang,et al.  Synchronization of nonidentical chaotic fractional-order systems with different orders of fractional derivatives , 2012, Nonlinear Dynamics.

[21]  W. Deng,et al.  Chaos synchronization of the fractional Lü system , 2005 .

[22]  Xiaomei Yan,et al.  Modified projective synchronization of fractional-order chaotic systems based on active sliding mode control , 2013, 2013 25th Chinese Control and Decision Conference (CCDC).

[23]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[24]  Liu Jin-Gui,et al.  A novel study on the impulsive synchronization of fractional-order chaotic systems , 2013 .

[25]  N. Arifin,et al.  Synchronization of two different fractional-order chaotic systems with unknown parameters using a robust adaptive nonlinear controller , 2016 .

[26]  Chunguang Li,et al.  Chaos in the fractional order Chen system and its control , 2004 .

[27]  Holger Voos,et al.  Observer-Based Approach for Fractional-Order Chaotic Synchronization and Secure Communication , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[28]  Juebang Yu,et al.  Chaos in the fractional order periodically forced complex Duffing’s oscillators , 2005 .

[29]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[30]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[31]  Sara Dadras,et al.  Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach ☆ , 2013 .

[32]  Guido Maione,et al.  Continued fractions approximation of the impulse response of fractional-order dynamic systems , 2008 .

[33]  Hongtao Lu,et al.  Synchronization of a new fractional-order hyperchaotic system , 2009 .

[34]  P Balasubramaniam,et al.  Sliding mode control for generalized robust synchronization of mismatched fractional order dynamical systems and its application to secure transmission of voice messages. , 2017, ISA transactions.

[35]  Hao Zhu,et al.  Chaos and synchronization of the fractional-order Chua’s system , 2009 .

[36]  Santanu Saha Ray,et al.  An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method , 2005, Appl. Math. Comput..

[37]  Ivo Petras,et al.  A note on the fractional-order Chua’s system , 2008 .

[38]  Yang Ge,et al.  Observer-based stabilisation of a class of fractional order non-linear systems for 0 α <;2 case , 2014 .

[39]  Elena Grigorenko,et al.  Erratum: Chaotic Dynamics of the Fractional Lorenz System [Phys. Rev. Lett.91, 034101 (2003)] , 2006 .

[40]  Hooman Fatoorehchi,et al.  Explicit Frost-Kalkwarf type equations for calculation of vapour pressure of liquids from triple to critical point by the Adomian decomposition method† , 2017 .

[41]  Jun-Guo Lu,et al.  Robust Stability and Stabilization of Fractional-Order Interval Systems with the Fractional Order $\alpha$: The $0≪\alpha≪1$ Case , 2010, IEEE Transactions on Automatic Control.

[42]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[43]  Chunguang Li,et al.  Chaos and hyperchaos in the fractional-order Rössler equations , 2004 .

[44]  Elena Grigorenko,et al.  Chaotic dynamics of the fractional Lorenz system. , 2003, Physical review letters.

[45]  P. Balasubramaniam,et al.  Synchronization and an application of a novel fractional order King Cobra chaotic system. , 2014, Chaos.

[46]  Saleh Mobayen,et al.  Secure communication in wireless sensor networks based on chaos synchronization using adaptive sliding mode control , 2017, Nonlinear Dynamics.

[47]  Nathalie Corson,et al.  Synchronization of Chaotic fractional-Order Systems via Linear Control , 2010, Int. J. Bifurc. Chaos.

[48]  Hadi Taghvafard,et al.  Phase and anti-phase synchronization of fractional order chaotic systems via active control , 2011 .

[49]  Jun-Guo Lu,et al.  Robust Stability and Stabilization of Fractional-Order Interval Systems: An LMI Approach , 2009, IEEE Transactions on Automatic Control.

[50]  Chun-Lai Li,et al.  Adaptive Sliding Mode Control for Synchronization of a Fractional-Order Chaotic System , 2013 .