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Tytuł:
Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities
Autorzy:
Vaidyanathan, S.
Volos, C.
Pham, V.-T.
Madhavan, K.
Idowu, B. A.
Powiązania:
https://bibliotekanauki.pl/articles/230036.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
jerk system
novel system
adaptive control
backstepping control
chaos synchronization
Opis:
In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as DKY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.
Źródło:
Archives of Control Sciences; 2014, 24, 3; 375-403
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control
Autorzy:
Vaidyanathan, S.
Powiązania:
https://bibliotekanauki.pl/articles/229916.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
chaotic systems
jerk systems
chaos control
adaptive control
backstepping control
synchronization
Opis:
This paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0:2974, L2 = 0 and L3 = −3:8974. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the new jerk chaotic system is found as DKY = 2:0763. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations are shown to illustrate all the main results derived in this work.
Źródło:
Archives of Control Sciences; 2017, 27, 3; 409-439
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new 4-D dynamical system exhibiting chaos with a line of rest points, its synchronizationand circuit model
Autorzy:
Vaidyanathan, Sundarapandian
Sambas, Aceng
Zhang, Sen
Powiązania:
https://bibliotekanauki.pl/articles/229283.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
chaotic systems
circuit design
synchronization
Opis:
A new 4-D dynamical system exhibiting chaos is introduced in this work. The proposed nonlinear plant with chaos has an unstable rest point and a line of rest points. Thus, the new nonlinear plant exhibits hidden attractors. A detailed dynamic analysis of the new nonlinear plant using bifurcation diagrams is described. Synchronization result of the new nonlinear plant with itself is achieved using Integral Sliding Mode Control (ISMC). Finally, a circuit modelusing MultiSim of the new 4-D nonlinear plant with chaos is carried out for practical use.
Źródło:
Archives of Control Sciences; 2019, 29, 3; 485-506
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities
Autorzy:
Vaidyanathan, S.
Powiązania:
https://bibliotekanauki.pl/articles/229724.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
hyperchaos
control
synchronization
Lyapunov exponents
Opis:
This research work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. We describe the qualitative properties of the novel 4-D hyperchaotic system and illustrate their phase portraits. We show that the novel 4-D hyperchaotic system has two unstable equilibrium points. The novel 4-D hyperchaotic system has the Lyapunov exponents L1 = 3.1575, L2 = 0.3035, L3 = 0 and L4 = −33.4180. The Kaplan-Yorke dimension of this novel hyperchaotic system is found as DKY = 3.1026. Since the sum of the Lyapunov exponents of the novel hyperchaotic system is negative, we deduce that the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to stabilize the novel 4-D hyperchaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 4-D hyperchaotic systems with unknown system parameters. The adaptive control results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this research work
Źródło:
Archives of Control Sciences; 2016, 26, 4; 471-495
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation
Autorzy:
Vaidyanathan, S.
Volos, C.
Pham, V.-T.
Powiązania:
https://bibliotekanauki.pl/articles/229321.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
hyperchaos
control
synchronization
circuit realization
Opis:
In this research work, a twelve-term novel 5-D hyperchaotic Lorenz system with three quadratic nonlinearities has been derived by adding a feedback control to a ten-term 4-D hyperchaotic Lorenz system (Jia, 2007) with three quadratic nonlinearities. The 4-D hyperchaotic Lorenz system (Jia, 2007) has the Lyapunov exponents L1 = 0.3684,L2 = 0.2174,L3 = 0 and L4 =−12.9513, and the Kaplan-Yorke dimension of this 4-D system is found as DKY =3.0452. The 5-D novel hyperchaotic Lorenz system proposed in this work has the Lyapunov exponents L1 = 0.4195,L2 = 0.2430,L3 = 0.0145,L4 = 0 and L5 = −13.0405, and the Kaplan-Yorke dimension of this 5-D system is found as DKY =4.0159. Thus, the novel 5-D hyperchaotic Lorenz system has a maximal Lyapunov exponent (MLE), which is greater than the maximal Lyapunov exponent (MLE) of the 4-D hyperchaotic Lorenz system. The 5-D novel hyperchaotic Lorenz system has a unique equilibrium point at the origin, which is a saddle-point and hence unstable. Next, an adaptive controller is designed to stabilize the novel 5-D hyperchaotic Lorenz system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 5-D hyperchaotic Lorenz systems with unknown system parameters. Finally, an electronic circuit realization of the novel 5-D hyperchaotic Lorenz system using SPICE is described in detail to confirm the feasibility of the theoretical model.
Źródło:
Archives of Control Sciences; 2014, 24, 4; 409-446
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs - application to chaos synchronization
Autorzy:
Moysis, Lazaros
Tripathi, Meenakshi
Gupta, Mahendra Kumar
Marwan, Muhammad
Volos, Christos
Powiązania:
https://bibliotekanauki.pl/articles/2106505.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
adaptive observer
incremental quadratic constraint
chaos synchronization
Opis:
This work addresses the problem of adaptive observer design for nonlinear systems satisfying incremental quadratic constraints. The output of the system includes nonlinear terms, which puts an additional strain on the design and feasibility of the observer, which is guaranteed under the satisfaction of an LMI, and a set of algebraic constraints. A particular case where the output nonlinearity matches the unknown parameter coefficient is also discussed. The result is illustrated through a numerical example for the chaos synchronization of the Rössler system.
Źródło:
Archives of Control Sciences; 2022, 32, 1; 105--121
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Probing 3D chaotic Thomas’ cyclically attractor with multimedia encryption and electronic circuitry
Autorzy:
Khan, NajeebAlam
Qureshi, Muhammad Ali
Akbar, Saeed
Ara, Asmat
Powiązania:
https://bibliotekanauki.pl/articles/27312000.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
Thomas’ cyclically attractor
fractional calculus
chaos
encryption
Opis:
This study investigates Thomas’ cyclically symmetric attractor dynamics with mathematical and electronic simulations using a proportional fractional derivative to comprehend the dynamics of a given chaotic system. The three-dimensional chaotic flow was examined in detail with Riemann-Liouville derivative for different values of the fractional index to highlight the sensitivity of chaotic systems with initial conditions. Thus, the dynamics of the fractional index system were investigated with Eigenvalues, Kaplan-Yorke dimension, Lyapunov exponent, and NIST testing, and their corresponding trajectories were visualized with phase portraits, 2D density plot, and Poincaré maps. After obtaining the results, we found that the integer index dynamics are more complex than the fractional index dynamics. Furthermore, the chaotic system circuit is simulated with operational amplifiers for different fractional indices to generate analog signals of the symmetric attractor, making it an important aspect of engineering. The qualitative application of our nonlinear chaotic system is then applied to encrypt different data types such as voice, image, and video, to ensure that the developed nonlinear chaotic system can widely applied in the field of cyber security.
Źródło:
Archives of Control Sciences; 2023, 33, 1; 239--271
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot
Autorzy:
Vaidyanathan, S.
Sambas, A.
Mamat, M.
Sanjaya, M.
Powiązania:
https://bibliotekanauki.pl/articles/229628.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
chaotic systems
hidden attractors
circuit simulation
Opis:
This research work proposes a new three-dimensional chaotic system with a hidden attractor. The proposed chaotic system consists of only two quadratic nonlinearities and the system possesses no critical points. The phase portraits and basic qualitative properties of the new chaotic system such as Lyapunov exponents and Lyapunov dimension have been described in detail. Finally, we give some engineering applications of the new chaotic system like circuit simulation and control of wireless mobile robot.
Źródło:
Archives of Control Sciences; 2017, 27, 4; 541-554
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear response of a harmonically driven oscillator in magnetic field
Autorzy:
Przybyłowicz, P.
Szmidt, T.
Powiązania:
https://bibliotekanauki.pl/articles/229889.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
nonlinear vibrations
oscillator
chaos
stability
magnetic damping
Opis:
The paper presents analysis of nonlinear response of a classical mechanical oscillator placed within a magnetic field and driven by a harmonic force. With an appropriate choice of control parameters, the system vibrates chaotically between different equilibrium positions. To prove this result, Lyapunov exponents have been calculated using the algorithm proposed by Rangarajan G., Habib S. and Ryne R.: Physical Review Letters, vol. 80, (1998). Moreover, the appropriate time series, phase portrait, Poincar'e cross-section and power spectrum are given to support the conclusion.
Źródło:
Archives of Control Sciences; 2010, 20, 1; 19-30
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Compound-combination synchronization of chaos in identical and different orders chaotic systems
Autorzy:
Ojo, K. S.
Njah, A. N.
Olusola, O. I.
Powiązania:
https://bibliotekanauki.pl/articles/229175.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
control and applications of chaos
low- and high-dimensional chaos
numerical simulations of chaotic models
synchronization
coupled oscillators
Opis:
This paper proposes a new synchronization scheme called compound-combination synchronization. The scheme is investigated using six chaotic Josephson junctions evolving from different initial conditions based on the drive-response configuration via the active backstepping technique. The technique is applied to achieve compound-combination synchronization of: (i) six identical third order resistive-capacitive-inductive-shunted Josepshon junctions (RCLSJJs) (with three as drive and three as response systems); (ii) three third order RCLSJJs (as drive systems) and three second order resistive-capacitive-shunted Josepshon junctions (RCSJJs (as response systems). In each case, sufficient conditions for global asymptotic stability for compound-combination synchronization to any desired scaling factors are achieved. Numerical simulations are employed to verify the feasibility and effectiveness of the compound-combination synchronization scheme. The result shows that this scheme could be used to vary the junction signal to any desired level and also give a better insight into synchronization in biological systems wherein different organs of different dynamical structures and orders are involved. The scheme could also provide high security in information transmission due to the complexity of its dynamical formulation.
Źródło:
Archives of Control Sciences; 2015, 25, 4; 463-490
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dynamics, control, stability, diffusion and synchronization of modified chaotic Colpitts oscillator
Autorzy:
Rasappan, Suresh
Niranjan Kumar, K. A.
Powiązania:
https://bibliotekanauki.pl/articles/1845526.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
Colpitts oscillator
Lyapunov exponent
diffusion
stability
synchronization
Opis:
The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
Źródło:
Archives of Control Sciences; 2021, 31, 3; 731-759
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dynamics, control, stability, diffusion and synchronization of modified chaotic Colpitts oscillator
Autorzy:
Rasappan, Suresh
Niranjan Kumar, K. A.
Powiązania:
https://bibliotekanauki.pl/articles/1845536.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
Colpitts oscillator
Lyapunov exponent
diffusion
stability
synchronization
Opis:
The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
Źródło:
Archives of Control Sciences; 2021, 31, 3; 731-759
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system
Autorzy:
Vaidyanathan, S.
Volos, C.
Powiązania:
https://bibliotekanauki.pl/articles/229285.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
chaotic system
conservative chaotic system
adaptive control
synchronization
Opis:
First, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1 = 0.0395, L2 = 0 and L3 = −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY =3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.
Źródło:
Archives of Control Sciences; 2015, 25, 3; 333-353
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new multi-stable chaotic hyperjerk system, its special features, circuit realization, control and synchronization
Autorzy:
Pham, Viet-Thanh
Vaidyanathan, Sundarapandian
Volos, Christos
Jafari, Sajad
Kapitaniak, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/229416.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
hyperjerk system
multi-stable
control
synchronization
circuit design
Opis:
Researchers have paid significant attention on hyperjerk systems, especial hyperjerk ones with chaos. A new hyperjerk system with seven terms and two parameters is analyzed. Chaotic attractors as well as coexisting attractors are displayed by the hyperjerk system. Thus it is a new multi-stable chaotic hyperjerk system. Further properties of the proposed hyperjerk system such as circuit design and backstepping-based control and synchronization are reported.
Źródło:
Archives of Control Sciences; 2020, 30, 1; 23-45
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based synchronization design and circuit simulation
Autorzy:
Vaidyanathan, Sundarapandian
Benkouider, Khaled
Sambas, Aceng
Powiązania:
https://bibliotekanauki.pl/articles/2106506.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
jerk systems
bifurcation
multistability
attractors
backstepping control
circuit design
Opis:
In this work, we present results for a new dissipative jerk chaotic system with three quadratic terms in its dynamics.We describe the bifurcation analysis for the new jerk system and also show that the proposed system exhibits multi-stability. Next, we describe a backstepping control-based synchronization design for a pair of new jerk chaotic systems. MATLAB simulations are put forth to exhibit the various findings in this work. Furthermore, we exhibit a circuit simulation for the new jerk system using MultiSim.
Źródło:
Archives of Control Sciences; 2022, 32, 1; 123--152
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 28

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