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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 velocity measurement method based on scaling parameter estimation of chaotic system
Autorzy:
Liu, L.
Hu, J.
He, Z.
Han, C.
Li, H.
Li, J.
Powiązania:
https://bibliotekanauki.pl/articles/220466.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
signal processing
parameter estimation
chaos
synchronization
Opis:
In this paper, we propose a new method of measuring the target velocity by estimating the scaling parameter of a chaos-generating system. First, we derive the relation between the target velocity and the scaling parameter of the chaos-generating system. Then a new method for scaling parameter estimation of the chaotic system is proposed by exploiting the chaotic synchronization property. Finally, numerical simulations show the effectiveness of the proposed method in target velocity measurement.
Źródło:
Metrology and Measurement Systems; 2011, 18, 2; 275-281
0860-8229
Pojawia się w:
Metrology and Measurement Systems
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:
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 chaotic system with axe-shaped equilibrium, its circuit implementation and adaptive synchronization
Autorzy:
Vaidyanathan, S.
Sambas, A.
Mamat, M.
Powiązania:
https://bibliotekanauki.pl/articles/230023.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
chaotic systems
curve equilibrium
Lyapunov exponents
circuit design
synchronization
Opis:
In the recent years, chaotic systems with uncountable equilibrium points such as chaotic systems with line equilibrium and curve equilibrium have been studied well in the literature. This reports a new 3-D chaotic system with an axe-shaped curve of equilibrium points. Dynamics of the chaotic system with the axe-shaped equilibrium has been studied by using phase plots, bifurcation diagram, Lyapunov exponents and Lyapunov dimension. Furthermore, an electronic circuit implementation of the new chaotic system with axe-shaped equilibrium has been designed to check its feasibility. As a control application, we report results for the synchronization of the new system possessing an axe-shaped curve of equilibrium points.
Źródło:
Archives of Control Sciences; 2018, 28, 3; 443-462
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control
Autorzy:
Vaidyanathan, S.
Powiązania:
https://bibliotekanauki.pl/articles/229836.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
dissipative chaotic system
chaos
chaotic system
adaptive control
backstepping control
synchronization
Opis:
This paper announces an eight-term novel 3-D jerk chaotic system with three quadratic 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 two equilibrium points, which are saddle-foci and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0.20572, L2 = 0 and L3 = −1.20824. 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 novel jerk chaotic system is derived as DKY = 2.17026. Next, an adaptive controller is designed via backstepping control method to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive controller is also designed via backstepping control method 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 have been depicted to illustrate the phase portraits of the novel jerk chaotic system and also the adaptive backstepping control results.
Źródło:
Archives of Control Sciences; 2016, 26, 1; 19-47
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new 4-D hyperchaotic system with no equilibrium, its multistability, offset boosting and circuit simulation
Autorzy:
Vaidyanathan, Sundarapandian
Moroz, Irene M.
Sambas, Aceng
Powiązania:
https://bibliotekanauki.pl/articles/229944.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
chaotic systems
hidden attractors
sliding mode control
circuit design
synchronization
Opis:
A new 4-D dynamical system with hyperchaos is reported in this work. It is shown that the proposed nonlinear dynamical system with hyperchaos has no equilibrium point. Hence, the new dynamical system exhibits hidden hyperchaotic attractor. An in-depth dynamic analysis of the new hyperchaotic system is carried out with bifurcation transition diagrams, multistability analysis, period-doubling bubbles and offset boosting analysis. Using Integral Sliding Mode Control (ISMC), global hyperchaos synchronization results of the new hyperchaotic system are described in detail. Furthermore, an electronic circuit realization of the new hyperchaotic system has been simulated in MultiSim software version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB.
Źródło:
Archives of Control Sciences; 2020, 30, 3; 575-597
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Synchronization of neuronal bursting using backstepping control with recursive feedback
Autorzy:
Rasappan, Suresh
Powiązania:
https://bibliotekanauki.pl/articles/229893.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Hindmarsh-Rose neuronal bursting system
chaos
synchronization
backstepping control
Lyapunov
stability
Opis:
J. L. Hindmarsh, R. M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.
Źródło:
Archives of Control Sciences; 2019, 29, 4; 617-642
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dynamical properties of a modified chaotic Colpitts oscillator with triangular wave non-linearity
Autorzy:
Suresh, Rasappan
Sathish Kumar, Kumaravel
Regan, Murugesan
Niranjan Kumar, K. A.
Narmada Devi, R.
Obaid, Ahmed J.
Powiązania:
https://bibliotekanauki.pl/articles/27312004.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
chaos
Colpitts oscillator
Lyapunov exponent
diffusion
stability
synchronization
triangular wave non-linearity
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 for triangular wave non-linearity. 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; 2023, 33, 1; 25--53
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 16

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