Dynamical analysis of a new multistable chaotic system with hidden attractor: Antimonotonicity, coexisting multiple attractors, and offset boosting

Bayani, Atiyeh; Rajagopal, Karthikeyan; Khalaf, Abdul Jalil M.; Jafari, Sajad; Leutcho, Gervais Dolvis; Kengne, Jacques

doi:10.1016/j.physleta.2019.02.005

Cited by 122 publications

(55 citation statements)

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“…This system is later transformed to a port Hamiltonian system which consider its energy properties. Besides, a chaotic system with hidden attractor [12] was used in this study for stabilization purposes, but before being transformed to a port Hamiltonian form. The results show that the system is stabilized better with our proposed control strategy in comparison with other strategies found in the literature.…”

Section: Discussionmentioning

confidence: 99%

“…The system (12) represented in port Hamiltonian form as shown in (13) with initial conditions X 0 = [2.5, 0, −1, −0.4, 0, 0, 0, 0] T yields the phase portraits as shown in Figure 3…”

Section: Problem Formulationmentioning

confidence: 99%

“…In this section, two numerical examples are shown. The first consists of the stabilization of the 2-D chaotic system (11) in port Hamiltonian form, and the second consists of the stabilization of a 4-D system (12) [12] represented in port Hamiltonian form. In the two experiment the proposed controller strategy is compared with the strategies shown in [25,29].…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Chaotic systems with hidden attractors have been extensively studied during recent years because the vast amount of physical systems in which this phenomenon is found [8][9][10][11]. Self-excited attractors are those kind in which the domain of attraction is at least one of the equilibrium points, whereas hidden attractors are those whereas the domain of attraction is not balanced [12]. In the literature there are many studies in which hidden attractors are analyzed, for example, in [13], a new 3-D chaotic system with hidden attractor is designed and analyzed in which the eigenvalues and Lyapunov exponents are obtained for dynamical analysis purposes.…”

Section: Introductionmentioning

confidence: 99%

“…The adaptive terminal sliding mode controller proposed in this paper is designed by establishing an appropriate sliding manifold to find the control law and then the adaptive control laws are obtained by selecting an appropriate Lyapunov function. The designed controller is used to balance a 2-D port Hamiltonian chaotic system, which was constructed according to the method shown in this paper and then a 4-D chaotic system with a hidden attractor as shown in [12].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stabilization of Port Hamiltonian Chaotic Systems with Hidden Attractors by Adaptive Terminal Sliding Mode Control

Azar

Serrano

2020

Entropy

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In this study, the design of an adaptive terminal sliding mode controller for the stabilization of port Hamiltonian chaotic systems with hidden attractors is proposed. This study begins with the design methodology of a chaotic oscillator with a hidden attractor implementing the topological framework for its respective design. With this technique it is possible to design a 2-D chaotic oscillator, which is then converted into port-Hamiltonia to track and analyze these models for the stabilization of the hidden chaotic attractors created by this analysis. Adaptive terminal sliding mode controllers (ATSMC) are built when a Hamiltonian system has a chaotic behavior and a hidden attractor is detected. A Lyapunov approach is used to formulate the adaptive device controller by creating a control law and the adaptive law, which are used online to make the system states stable while at the same time suppressing its chaotic behavior. The empirical tests obtaining the discussion and conclusions of this thesis should verify the theoretical findings.

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Section: Discussionmentioning

confidence: 99%

“…The system (12) represented in port Hamiltonian form as shown in (13) with initial conditions X 0 = [2.5, 0, −1, −0.4, 0, 0, 0, 0] T yields the phase portraits as shown in Figure 3…”

Section: Problem Formulationmentioning

confidence: 99%