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

Azar, Ahmad Taher; Serrano, Fernando E.

doi:10.3390/e22010122

Cited by 27 publications

(10 citation statements)

References 33 publications

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“…Due to the appropriate selection of the parameter values, the novel chaotic system enters in chaotic regimen considering that the initial conditions are crucial to find other domains of attractions in other equilibrium points. Because the domain of attraction in different equilibrium points of the novel chaotic systems is sensitive to the initial conditions, the initial conditions were chosen as long as they are close to the first encountered equilibrium point by determining that the inner product of two vector fields over the inner product of the initial condition and the equilibrium points is equal to infinity [ 82 ].…”

Section: Definition Of the Novel Chaotic Systemmentioning

confidence: 99%

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Azar

Serrano

Zhu

et al. 2021

Entropy

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In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

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Section: Definition Of the Novel Chaotic Systemmentioning

confidence: 99%

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Azar

Serrano

Zhu

et al. 2021

Entropy

Self Cite

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“…Human dynamics can resemble a multi-joint manipulator system and, accordingly, an alternative approach is to employ the adaptive control approach suggested for robotic systems [32][33][34][35]. By using a similar perspective, in this paper, instead of trajectory adaptation, we adapt the assistive torque profile of the exoskeleton while a low gain adaptive PD controller guarantees the stability of close loop during assistive torque adaptation.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Assistance Controller to Optimize the Exoskeleton Contribution in Rehabilitation

2021

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In this paper, we present a novel adaptation rule to optimize the exoskeleton assistance in rehabilitation tasks. The proposed method adapts the exoskeleton contribution to user impairment severity without any prior knowledge about the user motor capacity. The proposed controller is a combination of an adaptive feedforward controller and a low gain adaptive PD controller. The PD controller guarantees the stability of the human-exoskeleton system during feedforward torque adaptation by utilizing only the human-exoskeleton joint positions as the sensory feedback for assistive torque optimization. In addition to providing a convergence proof, in order to study the performance of our method we applied it to a simplified 2-DOF model of human-arm and a generic 9-DOF model of lower limb to perform walking. In each simulated task, we implemented the impaired human torque to be insufficient for the task completion. Moreover, the scenarios that violate our convergence proof assumptions are considered. The simulation results show a converging behavior for the proposed controller; the maximum convergence time of 20 s is observed. In addition, a stable control performance that optimally supplements the remaining user motor contribution is observed; the joint angle tracking error in steady condition and its improvement compared to the start of adaptation are as follows: shoulder 0.96±2.53° (76%); elbow −0.35±0.81° (33%); hip 0.10±0.86° (38%); knee −0.19±0.67° (25%); and ankle −0.05±0.20° (60%). The presented simulation results verify the robustness of proposed adaptive method in cases that differ from our mathematical assumptions and indicate its potentials to be used in practice.

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“…We deal with a hidden attractor when the mathematical model of a given system does not have a constant dynamic equilibrium point (stationary point). Previous literature reports on this subject concern both dynamic continuous systems (e.g., [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ]), and discrete multidimensional dynamic systems (for example: [ 26 , 27 , 28 , 29 , 30 ]). Research on this issue is crucial because it can protect the system from dangerous, chaotic oscillations.…”

Section: Introductionmentioning

confidence: 99%

Hidden Attractors in Discrete Dynamical Systems

Berezowski

Lawnik

2021

Entropy

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Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

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

Cited by 27 publications

References 33 publications

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

An Adaptive Assistance Controller to Optimize the Exoskeleton Contribution in Rehabilitation

Hidden Attractors in Discrete Dynamical Systems

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