Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique

Muñoz‐Pacheco, Jesús M.; Volos, Christos; Serrano, Fernando E.; Jafari, Sajad; Kengne, Jacques; Rajagopal, Karthikeyan

doi:10.3390/e23070921

Cited by 15 publications

(5 citation statements)

References 49 publications

(43 reference statements)

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“…Another control proposal is the fixed-time synchronization observer , which emphasizes the time of convergence of the error in the synchronization under complete error [ 35 ]. Finally, another control, back-stepping control , synchronizes two different systems with complete error by setting an extra variable [ 36 ].…”

Section: Related Workmentioning

confidence: 99%

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Zaqueros-Martinez

Gómez

Tlelo‐Cuautle

et al. 2023

Entropy

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Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi–Sugeno (T–S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

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Section: Related Workmentioning

confidence: 99%

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Zaqueros-Martinez

Gómez

Tlelo‐Cuautle

et al. 2023

Entropy

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“…With the use of the Bendixson theorem, a hidden attractor was found in a complex variable Lorenz chaotic system [51]. In this work, we discovered the hidden attractor by adding a disturbance term to the existing chaotic system, which could lead to the generation of a new system, but there is no universal method.…”

Section: New Hidden Chaotic System With Two Stable Equilibriamentioning

confidence: 99%

A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization

Wang

Dong

2022

Fractal Fract

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The study of hidden attractors plays a very important role in the engineering applications of nonlinear dynamical systems. In this paper, a new three-dimensional (3D) chaotic system is proposed in which hidden attractors and self-excited attractors appear as the parameters change. Meanwhile, asymmetric coexisting attractors are also found as a result of the system symmetry. The complex dynamical behaviors of the proposed system were investigated using various tools, including time-series diagrams, Poincaré first return maps, bifurcation diagrams, and basins of attraction. Moreover, the unstable periodic orbits within a topological length of 3 in the hidden chaotic attractor were calculated systematically by the variational method, which required six letters to establish suitable symbolic dynamics. Furthermore, the practicality of the hidden attractor chaotic system was verified by circuit simulations. Finally, offset boosting control and adaptive synchronization were used to investigate the utility of the proposed chaotic system in engineering applications.

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“…To suppress the chaos in PMSM drive system, an equivalent-inputdisturbance (EID) based control [12] was used to determine the stability region with local uniformly boundedness. For stability purpose, the fuzzy logic control technique is considered to an efficient conventional tool [13][14][15][16] using Nussbaum gain [17] and back-stepping technique [18,19]. With consideration of practical constraints, an adaptive back-stepping control approach was proposed by Zirkohi [20] to suppress the chaos phenomenon in PMSM with a time-varying barrier Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

Finite-time stability control with hardware-in-the-loop testing of a chaotic permanent magnet synchronous motor

Iqbal,

Bakhsh,

Singh

2024

Eng. Res. Express

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Stability of Permanent Magnet Synchronous Motor (PMSM) is of prime importance for the successful operation of the drive system, which is found to be dependent on initial operating conditions showing chaotic characteristic. Therefore, the paper presents the stabilization of a chaotic PMSM system through the finite-time stability approach. Form this aspect, three controllers have been developed which are effective for the suppression of machine chaotic behaviour. Proposed controllers are simpler and numerically stable in comparison with previous works. Furthermore, performance comparisons of the proposed controllers are also presented in term of their settling time and peak overshoot. Selection among the proposed controllers depends on the consideration of a particular operating index (settling time or peak overshoot) wherein, performance is also varies on system parameter λ. Performance evaluation of proposed controllers has been presented in MATLAB environment. In order to validate the obtained MATLAB results, a real-time analysis has been carried out using Typhoon Hardware-in-the-loop (HIL) emulator. The comparison shows that both results are follow the same trend and are closely coordinated with each other, which validates the proposed controllers.

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Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique

Cited by 15 publications

References 49 publications

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization

Finite-time stability control with hardware-in-the-loop testing of a chaotic permanent magnet synchronous motor

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