Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

Pérez-Cruz, J. Humberto; Tamayo-Meza, Pedro Alejandro; Figueroa, M.; Silva‐Ortigoza, Ramón; Ponce-Silva, Mario; Rivera-Blas, R.; Aldape-Pérez, Mario

doi:10.1155/2019/4706491

Cited by 17 publications

(8 citation statements)

References 59 publications

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“…Taking into account Lemma 1, Khalil [52] proposed a procedure to calculate the Lipschitz constant c [53]. Although this procedure produces conservative results, it is enough for the purpose of this work.…”

Section: Lipschitz Constant Determinationmentioning

confidence: 99%

A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System

et al. 2020

Self Cite

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The objective of this paper is to estimate the unmeasurable variables of a multistable chaotic system using a Luenberger-like observer. First, the observability of the chaotic system is analyzed. Next, a Lipschitz constant is determined on the attractor of this system. Then, the methodology proposed by Raghavan and the result proposed by Thau are used to try to find an observer. Both attempts are unsuccessful. In spite of this, a Luenberger-like observer can still be used based on a proposed gain. The performance of this observer is tested by numerical simulation showing the convergence to zero of the estimation error. Finally, the chaotic system and its observer are implemented using 32-bit microcontrollers. The experimental results confirm good agreement between the responses of the implemented and simulated observers.

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Section: Lipschitz Constant Determinationmentioning

confidence: 99%

A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System

et al. 2020

Self Cite

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“…In this regard, the control and synchronization of chaotic systems are also attracting a lot of attention [35][36][37][38]. For instance, Pérez-Cruz et al proposed a novel linear feedback controller for synchronization of chaotic master and slave systems [39]. In another study, Pérez-Cruz also proposed an adaptive control scheme for synchronization of uncertain systems [40].…”

Section: Introductionmentioning

confidence: 99%

Synchronization of a Non-Equilibrium Four-Dimensional Chaotic System Using a Disturbance-Observer-Based Adaptive Terminal Sliding Mode Control Method

Wang

Yousefpour

Yusuf

et al. 2020

Entropy

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In this paper, dynamical behavior and synchronization of a non-equilibrium four-dimensional chaotic system are studied. The system only includes one constant term and has hidden attractors. Some dynamical features of the governing system, such as invariance and symmetry, the existence of attractors and dissipativity, chaotic flow with a plane of equilibria, and offset boosting of the chaotic attractor, are stated and discussed and a new disturbance-observer-based adaptive terminal sliding mode control (ATSMC) method with input saturation is proposed for the control and synchronization of the chaotic system. To deal with unexpected noises, an extended Kalman filter (EKF) is implemented along with the designed controller. Through the concept of Lyapunov stability, the proposed control technique guarantees the finite time convergence of the uncertain system in the presence of disturbances and control input limits. Furthermore, to decrease the chattering phenomena, a genetic algorithm is used to optimize the controller parameters. Finally, numerical simulations are presented to demonstrate the performance of the designed control scheme in the presence of noise, disturbances, and control input saturation.

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“…Du et al [16] realized the multiple intelligent robot formation by a new nonlinear control protocol, where formation can be achieved in a finite time. In [17][18][19][20][21][22][23][24][25][26], the impacts of some practical factors including time delays, intermittent communications, and external disturbances on formation control and its practical applications, were well dealt with. Xiao et al [27] constructed nonlinear control protocols to realize finite-time formation for swarm systems with each agent modeled by a first-order integrator.…”

Section: Introductionmentioning

confidence: 99%

“…In [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], the formation regulation performance was not considered, which can be modeled as global suboptimal or optimal formation design problems. Inspired by the guaranteed-cost synchronization control for swarm systems addressed in [30], Wang et al [31] investigated guaranteedperformance formation control with limited communication.…”

Section: Introductionmentioning

confidence: 99%

Synchronization-Based Guaranteed-Performance Formation Design for Swarm Systems

Dang

Kong

et al. 2020

Complexity

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Guaranteed-performance formation control for swarm systems with the second-order dynamics is investigated based on the synchronization control strategy. Firstly, a new formation protocol is presented, where the weights of connected edges are adaptively regulated and the performance constraint is imposed. Then, on the basis of the Riccati inequality, sufficient conditions for synchronization-based guaranteed-performance formation are proposed, and an explicit expression of the guaranteed-performance cost is shown, where it is fully distributed to design gain matrices of the formation protocol in the sense that it is independent of global information of swarm systems. Moreover, the whole motion of a swarm system is determined, which is associated with initial states of all agents and formation control vectors. Finally, two numerical examples are shown to demonstrate theoretical conclusions, where the static whole motion and the dynamic whole motion are considered, respectively.

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Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

Cited by 17 publications

References 59 publications

A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System

A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System

Synchronization of a Non-Equilibrium Four-Dimensional Chaotic System Using a Disturbance-Observer-Based Adaptive Terminal Sliding Mode Control Method

Synchronization-Based Guaranteed-Performance Formation Design for Swarm Systems

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