GENERATING HYPERCHAOTIC ATTRACTORS WITH THREE POSITIVE LYAPUNOV EXPONENTS VIA STATE FEEDBACK CONTROL

2009 ◽  
Vol 19 (02) ◽  
pp. 651-660 ◽  
Author(s):  
GUOSI HU
Keyword(s):  
Lyapunov Exponents ◽  
State Feedback ◽  
Electronic Circuit ◽  
Three Dimensional ◽  
State Feedback Control ◽  
Hyperchaotic System ◽  
Lorenz Chaotic System ◽  
Simulation Results ◽  
New Hyperchaotic System ◽  
Good Agreement

This letter presents a new hyperchaotic system, which was obtained by adding a nonlinear quadratic controller to the first equation and a linear controller to the second equation of the three-dimensional autonomous modified Lorenz chaotic system. This system uses only two multipliers but can generate very complex strange attractors with three positive Lyapunov exponents. The system is not only demonstrated by numerical simulations but also implemented via an electronic circuit, showing very good agreement with the simulation results.

GENERATING HYPERCHAOTIC ATTRACTORS VIA APPROXIMATE TIME DELAYED STATE FEEDBACK

2008 ◽  
Vol 18 (11) ◽  
pp. 3485-3494 ◽  
Author(s):  
GUOSI HU ◽  
SHIQIN JIANG
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
State Feedback ◽  
Electronic Circuit ◽  
Hyperchaotic System ◽  
Lorenz Chaotic System ◽  
Simulation Results ◽  
Delayed State Feedback ◽  
New Hyperchaotic System ◽  
Good Agreement

This letter presents a new hyperchaotic system, which was constructed by adding an approximate time delayed state feedback to the second equation of Lorenz chaotic system. The constructed system is not only demonstrated by numerical simulations but also implemented via an electronic circuit, showing very good agreement with the simulation results.

GENERATING HYPERCHAOS VIA STATE FEEDBACK CONTROL

2005 ◽  
Vol 15 (10) ◽  
pp. 3367-3375 ◽  
Author(s):  
YUXIA LI ◽  
WALLACE K. S. TANG ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Computer Simulations ◽  
Chaotic System ◽  
Bifurcation Analysis ◽  
State Feedback ◽  
Electronic Circuit ◽  
Three Dimensional ◽  
State Feedback Control ◽  
Hyperchaotic System ◽  
Nonlinear State

In this letter, a simple nonlinear state feedback controller is designed for generating hyperchaos from a three-dimensional autonomous chaotic system. The hyperchaotic system is not only demonstrated by computer simulations but also verified with bifurcation analysis, and is implemented experimentally via an electronic circuit.

A New Five Dimensional Hyperchaotic System and its Fractional Order Form

2013 ◽  
Vol 464 ◽  
pp. 375-380 ◽  
Author(s):  
Ling Liu ◽  
Chong Xin Liu ◽  
Yi Fan Liao
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Simulation Analysis ◽  
Three Dimensional ◽  
Hyperchaotic System ◽  
Order Form ◽  
Simulation Results ◽  
Predictor Corrector ◽  
New Hyperchaotic System

In this paper, a new five-dimensional hyperchaotic system by introducing two additional states feedback into a three-dimensional smooth chaotic system. With three nonlinearities, this system has more than one positive Lyapunov exponents. Based on the fractional derivative theory, the fractional-order form of this new hyperchaotic system has been investigated. Through predictor-corrector algorithm, the system is proved by numerical simulation analysis. Simulation results are provided to illustrate the performance of the fractional-order hyperchaotic attractors well.

A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation

2018 ◽  
pp. 382-419 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Ahmad Taher Azar ◽  
Aceng Sambas ◽  
Shikha Singh ◽  
Kammogne Soup Tewa Alain ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Dissipative System ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Qualitative Properties ◽  
New Hyperchaotic System

This chapter announces a new four-dimensional hyperchaotic system having two positive Lyapunov exponents, a zero Lyapunov exponent, and a negative Lyapunov exponent. Since the sum of the Lyapunov exponents of the new hyperchaotic system is shown to be negative, it is a dissipative system. The phase portraits of the new hyperchaotic system are displayed with both two-dimensional and three-dimensional phase portraits. Next, the qualitative properties of the new hyperchaotic system are dealt with in detail. It is shown that the new hyperchaotic system has three unstable equilibrium points. Explicitly, it is shown that the equilibrium at the origin is a saddle-point, while the other two equilibrium points are saddle-focus equilibrium points. Thus, it is shown that all three equilibrium points of the new hyperchaotic system are unstable. Numerical simulations with MATLAB have been shown to validate and demonstrate all the new results derived in this chapter. Finally, a circuit design of the new hyperchaotic system is implemented in MultiSim to validate the theoretical model.

scholarly journals Output Regulation of the Pan System

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
V. Sundarapandian
Keyword(s):  
Feedback Control ◽  
Secure Communication ◽  
State Feedback ◽  
Three Dimensional ◽  
Output Regulation ◽  
State Feedback Control ◽  
Chaotic Attractors ◽  
Control Laws ◽  
Potential Applications ◽  
Simulation Results

We solve the problem of regulating the output of the Pan system (2010), which is one of the recently discovered three-dimensional chaotic attractors. Pan system has many interesting complex dynamical behaviours, and it has potential applications in secure communication. In this paper, we construct explicit state feedback control laws for regulating the output of the Pan system so as to track constant reference signals. The state feedback control laws are derived using the regulator equations of Byrnes and Isidori (1990). The simulation results are provided to illustrate the effectiveness of the regulation schemes derived for the output regulation of the Pan system.

A NEW HYPERCHAOTIC SYSTEM AND ITS CIRCUIT IMPLEMENTATION

2010 ◽  
Vol 20 (04) ◽  
pp. 1201-1208 ◽  
Author(s):  
MINGHUA LIU ◽  
JIUCHAO FENG ◽  
CHI K. TSE
Keyword(s):  
Nonlinear Control ◽  
Bifurcation Diagram ◽  
Continuous Time ◽  
Control Parameter ◽  
Electronic Circuit ◽  
Three Dimensional ◽  
Hyperchaotic System ◽  
Circuit Implementation ◽  
Time Autonomous ◽  
New Hyperchaotic System

A four-dimensional continuous-time autonomous hyperchaotic system is proposed in this letter. This system is constructed by incorporating a nonlinear control to a three-dimensional continuous-time autonomous chaotic system. The hyperchaotic system is analyzed by studying the spectrum of Lyapunov exponents and the corresponding bifurcation diagram. The system exhibits chaotic, periodic, hyperchaotic behaviors for different values of a selected control parameter. Also, a simple electronic circuit is designed and implemented. Simulations and experimental observations verify the analytical results.

A New 4D Four-Wing Memristive Hyperchaotic System: Dynamical Analysis, Electronic Circuit Design, Shape Synchronization and Secure Communication

2020 ◽  
Vol 30 (10) ◽  
pp. 2050147 ◽  
Author(s):  
Fei Yu ◽  
Shuai Qian ◽  
Xi Chen ◽  
Yuanyuan Huang ◽  
Li Liu ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Secure Communication ◽  
Electronic Circuit ◽  
Mathematical Structure ◽  
Dynamical Analysis ◽  
Hyperchaotic System ◽  
Chen System ◽  
Information Signal ◽  
Communication Scheme ◽  
Good Agreement

In this paper, a simple four-wing chaotic attractor is first proposed by replacing the constant parameters of the Chen system with a periodic piecewise function. Then, a new 4D four-wing memristive hyperchaotic system is presented by adding a flux-controlled memristor with linear memductance into the proposed four-wing Chen system. The memristor mathematical structure model is simple and easy to implement. Dynamical analysis and numerical simulation of the memristive hyperchaotic system are carried out. Then, the electronic circuit of the hyperchaotic system is designed and implemented. The results of numerical simulation are in good agreement with the electronic circuit experiment. In addition, shape synchronization control for the 4D four-wing memristive hyperchaotic system is realized, and a communication system is designed by using the shape synchronization method. Finally, secure signal masking application is implemented on Matlab platform. In the developed secure communication scheme, the information signal overlaps with the chaotic masking signal, which improves the security of the system.

Dynamic Analysis and Three-Dimensional Finite Element Simulation of Cracked Gear

2007 ◽  
Vol 353-358 ◽  
pp. 1072-1077 ◽  
Author(s):  
Ren Ping Shao ◽  
Xin Na Huang ◽  
Pu Rong Jia ◽  
Wan Lin Guo ◽  
Kaoru Hirota
Keyword(s):  
Fault Diagnosis ◽  
Gear Tooth ◽  
Three Dimensional ◽  
Dynamic Features ◽  
Cracked Beam ◽  
Element Simulation ◽  
Dimensional Finite Element ◽  
Simulation Results ◽  
Three Dimensional Finite Element ◽  
Good Agreement

A method of damage detection and fault diagnosis for gears is presented based on the theory of elastomeric dynamics according to the theory of cracked beam. It takes an advantage of accurate fault diagnosis of gear body using the change of dynamic features and has some advantages for dynamic design of gear systems.The dynamics characteristics, i.e., natural frequency, vibration shape,dynamic response and so on, due to crack of gear tooth are studied, and the gear dynamics characteristics caused by the position and size of crack are deeply investigated by comparison with FEM. The theoretical analysis results are contrasted with numerical simulation results and shows good agreement with the result by FEM. The proposed method can be used to detect damage and diagnose fault for gear structures and also can be applied to designing dynamic characteristics for gear systems.

Advanced Model-Based Disturbance Compensation Control Using Proportional-Integral-Observer

2005 ◽  
Author(s):  
Idriz Krajcin ◽  
Dirk So¨ffker
Keyword(s):  
State Feedback ◽  
Dynamical Behavior ◽  
State Feedback Control ◽  
Disturbance Compensation ◽  
Proportional Integral ◽  
Compensation Control ◽  
Model Based ◽  
Simulation Results ◽  
And Control ◽  
Advanced Model

This contribution presents a state feedback control and a new disturbance compensation method using the Proportional-Integral-Observer (PI-Observer). For a suitable class of systems the observer estimates the unmeasured states as well as unknown inputs acting on a structure using a small number of measurements. Here, the observer is applied to elastic structures where the PI-Observer can be used for model-based diagnosis and control. An extended disturbance compensation is proposed to improve the dynamical behavior, to decouple the effect of disturbances on defined outputs using the PI-Observer. The observer and the control are applied to an all side clamped elastic plate. The performance of the control is illustrated by simulation results.

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