A Chaotic System with Infinite Number of Equilibria Located on an Exponential Curve and Its Chaos-Based Engineering Application

Mobayen, Saleh; Volos, Christos; Kaçar, Sezgin; Çavuşoğlu, Ünal; Vaseghi, Behrouz

doi:10.1142/s0218127418501122

Cited by 26 publications

(12 citation statements)

References 53 publications

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“…The suggested observer-based control scheme needs only Cartesian position measurement. [28][29][30][31][32][33][34][35] The contributions of this paper lie in twofold. Firstly, proposing a new Enhanced Fruit fly optimization (EFFO) algorithm.…”

Section: Introductionmentioning

confidence: 99%

Trajectory tracking of differential drive mobile robots using fractional-order proportional-integral-derivative controller design tuned by an enhanced fruit fly optimization

Abed

Rashid

Abedi

et al. 2022

Measurement and Control

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This work proposes a new kind of trajectory tracking controller for the differential drive mobile robot (DDMR), namely, the nonlinear neural network fractional-order proportional integral derivative (NNFOPID) controller. The suggested controller’s coefficients comprise integral, proportional, and derivative gains as well as derivative and integral powers. The adjustment of these coefficients turns the design of the proposed NNFOPID control further problematic than the conventional proportional-integral-derivative control. To handle this issue, an Enhanced Fruit Fly Swarm Optimization algorithm has been developed and proposed in this work to tune the NNFOPID’s parameters. The enhancement achieved on the standard fruit fly optimization technique lies in the increased uncertainty in the values of the initialized coefficients to convey a broader search space. subsequently, the search range is varied throughout the updating stage by beginning with a big radius and declines gradually during the course of the searching stage. The proposed NNFOPID controller has been validated its ability to track specific three types of continuous trajectories (circle, line, and lemniscate) while minimizing the mean square error and the control energy. Demonstrations have been run under MATLAB environment and revealed the practicality of the designed NNFOPID motion controller, where its performance has been compared with that of a nonlinear Neural Network Proportional Integral Derivative controller on the tracking of one of the aforementioned trajectories of the DDMR.

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Section: Introductionmentioning

confidence: 99%

Trajectory tracking of differential drive mobile robots using fractional-order proportional-integral-derivative controller design tuned by an enhanced fruit fly optimization

Abed

Rashid

Abedi

et al. 2022

Measurement and Control

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show abstract

Section: Introductionmentioning

confidence: 99%

“…14 Delayed-feedback control has been used for a chaotic traffic flow system with possible applications in the efficient design of road traffic. 15 Different techniques of chaos control have been applied in the areas of image encryption [16][17][18][19][20] and data security, [21][22][23] among other techniques and applications. [24][25][26][27][28] In most computational studies of chaos control found in the literature, no arbitrary precision has been used during the simulations.…”

Section: Introductionmentioning

confidence: 99%

Computational chaos control based on small perturbations for complex spectra simulation

et al. 2022

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In this paper, we propose to use a computational method of chaos control to simulate complex experimental spectra. This computational chaos control technique is based on the Ott–Grebogi–York (OGY) method. We chose the logistic map as the base mathematical model for the development of our work. For the numeric part, we created arbitrary precision algorithms to generate the solutions. This way, we completely eliminated any degradation of chaos from our results. These algorithms were also necessary for the proper perturbation process that the computational chaos control method requires. We control the chaos of the logistic map in two cases of Period 1 and one case of Period 2 to demonstrate that our control method works. The behavior of a complex experimental spectrum was taken and numerically simulated. The simulated spectrum was obtained by controlling the chaos of the logistic map in a variable way with the methods proposed in this work. Our results show that it is possible to simulate very complicated experimental spectra by computationally controlling the chaos of an equation unrelated to the experimental system.

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“…e research on chaos and chaos control has been greatly developed and widely used. A lot of valuable research results have been obtained in [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method

Guo

Ding²,

Li³

2021

Discrete Dynamics in Nature and Society

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The dynamics behavior of a discrete-time three-species food chain model is investigated. By using bifurcation theory, it is shown that the equilibrium point of the system loses its stability, and the system undergoes Neimark–Sacker bifurcation, which leads to chaos as the parameter changes. The chaotic motion is controlled on the stable periodic period-1 orbit using the implementation of the hybrid control strategy. The factor affecting the control time of chaos is also studied. Numerical simulations are consistent with the theoretical analysis. The results of this research prove that the chaos control method can be extended to the higher-dimensional biological model and can be realized.

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A Chaotic System with Infinite Number of Equilibria Located on an Exponential Curve and Its Chaos-Based Engineering Application

Cited by 26 publications

References 53 publications

Trajectory tracking of differential drive mobile robots using fractional-order proportional-integral-derivative controller design tuned by an enhanced fruit fly optimization

Trajectory tracking of differential drive mobile robots using fractional-order proportional-integral-derivative controller design tuned by an enhanced fruit fly optimization

Computational chaos control based on small perturbations for complex spectra simulation

Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method

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