Synchronization of chaotic Akgul system by means of feedback linearization and pole placement

Cruz, José Humberto Pérez; Figueroa, M.; Paredes, Salvador Antonio Rodríguez; Villa, A. López

doi:10.1109/tla.2017.7854619

Cited by 8 publications

(7 citation statements)

References 50 publications

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“…This myth vanished in 1983 thanks to Yamada and Fujisaka [6] where a methodology for the synchronization of two chaotic systems using bidirectional coupling is presented, meanwhile in 1990 Pecora and Carroll [7] proposed the synchronization of the drive and response systems with different initial conditions. Since then, a wide series of alternative methodologies for the synchronization of chaotic systems have been developed [8][9][10][11][12][13][14][15][16] and thanks to this methodologies, a vast quantity of possible applications have been found in science and engineering, from physics [17,18], optics [19,20], biology [21][22][23], chemistry [24,25] and specially in the branch of secure communications [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

Pulido-Luna

López-Rentería

Cázarez-Castro

2020

MCA

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In this work, a generalization of a synchronization methodology applied to a pair of chaotic systems with heterogeneous dynamics is given. The proposed control law is designed using the error state feedback and Lyapunov theory to guarantee asymptotic stability. The control law is used to synchronize two systems with different number of scrolls in their dynamics and defined in a different number of pieces. The proposed control law is implemented in an FPGA in order to test performance of the synchronization schemes.

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Section: Introductionmentioning

confidence: 99%

Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

Pulido-Luna

López-Rentería

Cázarez-Castro

2020

MCA

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“…The problem of the unidirectional synchronization of chaotic systems consists of finding an appropriate control law such that when this is applied to a system with coupled inputs called "slave" or "response," such system follows the dynamics of an autonomous chaotic system called "master" or "drive" [1][2][3][4][5][6][7][8][9][10][11]. This proper control action is necessary because, without it, two identical autonomous chaotic systems could never be synchronized due to their high sensitivity to initial conditions [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

et al. 2019

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In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach.

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“…Adaptable control [16][17][18][19]26,27] is of interest for the synchronization of chaotic systems because of the presence of unknown parameters since the learning laws are continuously updated for maintaining the performance of the system. Other controls are also applied, for example the control by state feedback [28][29][30][31][32][33][34], feedback control with delays [35][36][37][38] or active control [39][40][41][42] which works by considering the error synchronization, here the nonlinearities are eliminated, and the dynamic error equations are decoupled. Finally, synchronization has been used through neural networks [43].…”

Section: Introductionmentioning

confidence: 99%

Design and Implementation of a Microcontroller Based Active Controller for the Synchronization of the Petrzela Chaotic System

et al. 2019

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This paper presents an active control design for the synchronization of two identical Petrzela chaotic systems (Petrzela, J.; Gotthans, T. New chaotic dynamical system with a conic-shaped equilibrium located on the plane structure. Applied Sciences. 2017, 7, 976) on master-slave configuration. For the active control, the parameters of both systems are assumed to be a priori known, the control law by means of the dynamic of the error synchronization is designed to guarantee the convergence to zero of error states and the synchronization process is verified by numerical simulation. By taking advantage of the execution and implementation facilities of microcontroller based chaotic systems in digital devices, the active controller is implemented in a 32 bits ARM microcontroller. The experimental results were obtained by using the fourth order Runge-Kutta numerical method to integrate the differential equations of the controller, where the results were measured with a digital oscilloscope.

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Synchronization of chaotic Akgul system by means of feedback linearization and pole placement

Cited by 8 publications

References 50 publications

Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

Design and Implementation of a Microcontroller Based Active Controller for the Synchronization of the Petrzela Chaotic System

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