Design of a nonlinear controller and its intelligent optimization for exponential synchronization of a new chaotic system

Pérez-Cruz, J. Humberto; Portilla-Flores, Edgar Alfredo; Niño-Suárez, Paola Andrea; Rivera-Blas, R.

doi:10.1016/j.ijleo.2016.10.140

Cited by 10 publications

(14 citation statements)

References 57 publications

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“…Chaotic systems are nonlinear aperiodic oscillators with high sensitivity to initial conditions. Due to above, in recent years, the study of chaotic systems has increased because of their different applications in various areas of engineering [1]. In 1963, Edward N. Lorenz developed the first chaotic system of third order Ordinary Differential Equations (ODE).…”

Section: Introductionmentioning

confidence: 99%

“…In this context, the dynamic behavior of two systems must converge on the same unique chaotic behavior. These two systems can be coupled unidirectionally, also so-called master-slave configuration, i.e., the autonomous system with hyperchaotic dynamics is called master and the another system, which is forced to follow the hyperchaotic behavior by coupled inputs, called slave [1].…”

Section: Introductionmentioning

confidence: 99%

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Chaos Synchronization for Hyperchaotic Lorenz-Type System via Fuzzy-Based Sliding-Mode Observer

Plata

Prieto

Ramirez-Villalobos

et al. 2020

MCA

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Hyperchaotic systems have applications in multiple areas of science and engineering. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. In order to solve the chaos synchronization problem for a hyperchaotic Lorenz-type system, we propose an observer based synchronization under a master-slave configuration. The proposed methodology consists of designing a sliding-mode observer (SMO) for the hyperchaotic system. In contrast, this type of methodology exhibits high-frequency oscillations, commonly known as chattering. To solve this problem, a fuzzy-based SMO system was designed. Numerical simulations illustrate the effectiveness of the synchronization between the hyperchaotic system obtained and the proposed observer.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Chaos Synchronization for Hyperchaotic Lorenz-Type System via Fuzzy-Based Sliding-Mode Observer

Plata

Prieto

Ramirez-Villalobos

et al. 2020

MCA

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show abstract

“…Another approach is nonlinear control [33][34][35][36][37][38][39][40]. In this technique, given a Lyapunov function candidate , the control law is selected considering that the first derivative of must be compelled to be negative definite [41]. Hence, the asymptotic convergence to zero of the synchronization error can be guaranteed.…”

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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“…This began due to the work of references [1,2] in which they showed that synchronization of chaotic systems is possible; this development has been utilized in areas such as secure communications [3][4][5], cryptography [6,7], medical applications, mechanisms, and robotics [8][9][10][11][12][13][14][15]. Some of the synchronization schemes that have been successfully developed and applied include linear and nonlinear feedback control [16][17][18][19][20][21][22][23][24][25], where a Lyapunov candidate function V is proposed in such a way that the control law selected from the first derivative of V must be defined as negative [25]. 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.…”

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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Design of a nonlinear controller and its intelligent optimization for exponential synchronization of a new chaotic system

Cited by 10 publications

References 57 publications

Chaos Synchronization for Hyperchaotic Lorenz-Type System via Fuzzy-Based Sliding-Mode Observer

Chaos Synchronization for Hyperchaotic Lorenz-Type System via Fuzzy-Based Sliding-Mode Observer

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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