Multi-switching synchronization of nonlinear hyperchaotic systems via backstepping control

Abstract This chapter presents the multi-switching synchronization of nonlinear hyperchaotic systems via active backstepping control. The multi-switching complete synchronization scheme has been examined such that the state variables of slave system synchronize with different state variables of master system. The controllers are computed via active backstepping control design and Lyapunov stability criteria is used to ensure the stability of the dynamical system. To perform this methodology a hyperchaotic system is considered and it is applied on three switches. Numerical simulation results are performed to demonstrate the validity and feasibility of the applied method.

[1]  Ahmad Taher Azar,et al.  Fractional-Order Control Scheme for Q-S Chaos Synchronization , 2019, AMLTA.

[2]  Ahmad Taher Azar,et al.  A New Control Scheme for Hybrid Chaos Synchronization , 2018, AISI.

[3]  Shikha Singh,et al.  New Control Schemes for Fractional Chaos Synchronization , 2018, AISI.

[4]  Shikha Ayub Khan Mixed Tracking and Projective Synchronization of 6 D Hyperchaotic System Using Active Control , 2016 .

[5]  Sundarapandian Vaidyanathan,et al.  Dynamics Analysis and Synchronization in Relay Coupled Fractional Order Colpitts Oscillators , 2018 .

[6]  Ahmad Taher Azar,et al.  Combination-Combination Anti-Synchronization of Four Fractional Order Identical Hyperchaotic Systems , 2019, AMLTA.

[7]  Shikha Singh,et al.  Sliding mode control technique for multi-switching synchronization of chaotic systems , 2017, 2017 9th International Conference on Modelling, Identification and Control (ICMIC).

[8]  Ahmad Taher Azar,et al.  Dynamics, Synchronization and Fractional Order Form of a Chaotic System With Infinite Equilibria , 2018 .

[9]  Akif Akgul,et al.  A memristor-based system with hidden hyperchaotic attractors, its circuit design, synchronisation via integral sliding mode control and an application to voice encryption , 2019, Int. J. Autom. Control..

[10]  Viet-Thanh Pham,et al.  Synchronisation of integer-order and fractional-order discrete-time chaotic systems , 2019, Pramana.

[11]  George S. Tombras,et al.  A Novel Chaotic System without Equilibrium: Dynamics, Synchronization, and Circuit Realization , 2017, Complex..

[12]  Ahmad Taher Azar,et al.  Chaotic Control in Fractional-Order Discrete-Time Systems , 2019, AISI.

[13]  Ahmad Taher Azar,et al.  Stabilization of Port Hamiltonian Chaotic Systems with Hidden Attractors by Adaptive Terminal Sliding Mode Control , 2020, Entropy.

[14]  Ahmad Taher Azar,et al.  Control and Synchronization of a Fractional Order Hyperchaotic System via Backstepping and Active Backstepping Approach , 2018 .

[15]  Shikha Singh,et al.  Multi-switching Master–Slave Synchronization of Non-identical Chaotic Systems , 2018 .

[16]  Haijun Jiang,et al.  General Decay Lag Synchronization for Competitive Neural Networks with Constant Delays , 2019, Neural Processing Letters.

[17]  Sundarapandian Vaidyanathan,et al.  A New Method to Synchronize Fractional Chaotic Systems with Different Dimensions , 2017, Fractional Order Control and Synchronization of Chaotic Systems.

[18]  Shikha,et al.  Dynamical behavior and reduced-order combination synchronization of a novel chaotic system , 2018 .

[19]  A. Azar,et al.  A robust method for new fractional hybrid chaos synchronization , 2017 .

[20]  Ahmad Taher Azar,et al.  Stability analysis and robust synchronisation of fractional-order modified Colpitts oscillators , 2020, Int. J. Autom. Control..

[21]  Sundarapandian Vaidyanathan,et al.  New hybrid synchronisation schemes based on coexistence of various types of synchronisation between master-slave hyperchaotic systems , 2017, Int. J. Comput. Appl. Technol..

[22]  Ahmad Taher Azar,et al.  Dead-beat synchronization control in discrete-time chaotic systems , 2017, 2017 6th International Conference on Modern Circuits and Systems Technologies (MOCAST).

[23]  Xikui Ma,et al.  Synchronization control of cross-strict feedback hyperchaotic system based on cross active backstepping design , 2007 .

[24]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[25]  Ahmad Taher Azar,et al.  On Inverse Full State Hybrid Function Projective Synchronization For Continuous-time Chaotic Dynamical Systems with Arbitrary Dimensions , 2020 .

[26]  Shikha,et al.  Hybrid function projective synchronization of chaotic systems via adaptive control , 2017 .

[27]  Ahmad Taher Azar,et al.  A New Generalized Synchronization Scheme to Control Fractional Chaotic Systems with Non-identical Dimensions and Different Orders , 2019, AMLTA.

[28]  Hongyue Du,et al.  Modified function projective synchronization of chaotic system , 2009 .

[29]  Shikha,et al.  Combination synchronization of Genesio time delay chaotic system via robust adaptive sliding mode control , 2018 .

[30]  Sundarapandian Vaidyanathan,et al.  On New Fractional Inverse Matrix Projective Synchronization Schemes , 2017, Fractional Order Control and Synchronization of Chaotic Systems.

[31]  Ahmad Taher Azar,et al.  Four-wing attractors in a novel chaotic system with hyperbolic sine nonlinearity , 2017 .

[32]  M. Bettayeb,et al.  A novel secure image transmission scheme based on synchronization of fractional-order discrete-time hyperchaotic systems , 2017 .

[33]  Ahmad Taher Azar,et al.  A 4-D chaotic hyperjerk system with a hidden attractor, adaptive backstepping control and circuit design , 2023, Archives of Control Sciences.

[34]  Ahmad Taher Azar,et al.  Robust observer-based synchronisation of chaotic oscillators with structural perturbations and input nonlinearity , 2019, Int. J. Autom. Control..

[35]  Sundarapandian Vaidyanathan,et al.  Fractional Inverse Generalized Chaos Synchronization Between Different Dimensional Systems , 2017, Fractional Order Control and Synchronization of Chaotic Systems.

[36]  Zhen Wang Synchronization of an Uncertain Fractional-Order Chaotic System via Backstepping Sliding Mode Control , 2013 .

[37]  Ana Dalia Pano-Azucena,et al.  Arduino-based chaotic secure communication system using multi-directional multi-scroll chaotic oscillators , 2016, Nonlinear Dynamics.

[38]  Quanmin Zhu,et al.  Synchronization Between a Novel Integer-Order Hyperchaotic System and a Fractional-Order Hyperchaotic System Using Tracking Control , 2018, 2018 10th International Conference on Modelling, Identification and Control (ICMIC).

[39]  Sundarapandian Vaidyanathan,et al.  Hyperchaos and Adaptive Control of a Novel Hyperchaotic System with Two Quadratic Nonlinearities , 2017, Fractional Order Control and Synchronization of Chaotic Systems.

[40]  Muzaffar Ahmad Bhat,et al.  Complete synchronisation of non-identical fractional order hyperchaotic systems using active control , 2019, Int. J. Autom. Control..

[41]  Abdesselem Boulkroune,et al.  A novel 4-D hyperchaotic system with two quadratic nonlinearities and its adaptive synchronisation , 2018, Int. J. Autom. Control..

[42]  Sundarapandian Vaidyanathan,et al.  Global chaos synchronisation of identical chaotic systems via novel sliding mode control method and its application to Zhu system , 2015, Int. J. Model. Identif. Control..

[43]  Jie Xiao,et al.  Generalized Synchronization Between Chen System and Rucklidge System , 2019, IEEE Access.

[44]  Fang Wang,et al.  Generalized projective synchronization for networks with one crucial node and different dimensional nodes via a single controller , 2019, Asian Journal of Control.

[45]  Mitsuru Kikuchi,et al.  Changes in functional connectivity dynamics with aging: A dynamical phase synchronization approach , 2019, NeuroImage.

[46]  Ahmad Taher Azar,et al.  A Study on Coexistence of Different Types of Synchronization Between Different Dimensional Fractional Chaotic Systems , 2017, Fractional Order Control and Synchronization of Chaotic Systems.

[47]  Ahmad Taher Azar,et al.  Control of continuous-time chaotic (hyperchaotic) systems: F-M synchronisation , 2019, Int. J. Autom. Control..

[48]  Shihua Chen,et al.  Adaptive control for anti-synchronization of Chua's chaotic system , 2005 .

[49]  Ahmad Taher Azar,et al.  Synchronization Phenomena in Coupled Dynamical Systems with Hidden Attractors , 2018 .

[50]  Shikha Singh,et al.  Controlling Chaotic System via Optimal Control , 2019, AISI.

[51]  Ahmad Taher Azar,et al.  A new type of hybrid synchronization between arbitrary hyperchaotic maps , 2016, International Journal of Machine Learning and Cybernetics.

[52]  Karl E. Lonngren,et al.  Multi-switching synchronization of chaotic systems with active controllers , 2008 .

[53]  Ahmad Taher Azar,et al.  Enhanced Fractional Order Indirect Fuzzy Adaptive Synchronization of Uncertain Fractional Chaotic Systems Based on the Variable Structure Control , 2018 .

[54]  Sundarapandian Vaidyanathan,et al.  Active Control for Multi-Switching Combination Synchronization of Non-Identical Chaotic Systems , 2018 .

[55]  Sundarapandian Vaidyanathan,et al.  Design and SPICE implementation of a 12-term novel hyperchaotic system and its synchronisation via active control , 2015, Int. J. Model. Identif. Control..

[56]  Ahmad Taher Azar,et al.  Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators , 2018, Complex..

[57]  Sundarapandian Vaidyanathan,et al.  A Three-Dimensional No-Equilibrium Chaotic System: Analysis, Synchronization and Its Fractional Order Form , 2017, Fractional Order Control and Synchronization of Chaotic Systems.

[58]  Shikha,et al.  Increased and Reduced Order Synchronisations between 5D and 6D Hyperchaotic Systems , 2017 .

[59]  Ahmad Taher Azar,et al.  Generalized Synchronization of Different Dimensional Integer-Order and Fractional Order Chaotic Systems , 2017, Fractional Order Control and Synchronization of Chaotic Systems.