The aim of this paper is to study the control of hyperchaofic complex nonlinear systems with unknown parameters using passive control theory. An approach is stated to design the passive controller and estimate the unk...The aim of this paper is to study the control of hyperchaofic complex nonlinear systems with unknown parameters using passive control theory. An approach is stated to design the passive controller and estimate the unknown parameters based on the property of the passive system. The feasibility and effectiveness of the proposed approach is demonstrated through its application to the hyperchaotic complex Lu system, as an example. The estimated values of the unknown parameters are calculated. The analytical form of the complex controller is derived and used in the numerical simulation to control the hyperchaotic attractors of this example. Block diagrams of this example using Matlab/Simulink are constructed after and before the control to ensure the validity of the analytical results. Other examples of hyperchaotic complex nonlinear systems can be similarly treated.展开更多
This paper investigates the adaptive synchronization of hyperchaotic Lii systems based on the method of extended passive control. By combining the feedback control, the extended passive control method with two output ...This paper investigates the adaptive synchronization of hyperchaotic Lii systems based on the method of extended passive control. By combining the feedback control, the extended passive control method with two output variables is developed, which can synchronize hyperchaotic Lu systems asymptotically and globally more easily without knowing the bound of state of the hyperchaotic system. Adaptive laws are introduced to estimate the unknown parameters as well. Simulation results show the effectiveness and flexibility of the proposed control scheme.展开更多
Synchronization of a hyperchaotic Lorenz system is discussed using passive control. Based on the properties of a passive system, a passive controller is designed and the synchronization between two hyperchaotic Lorenz...Synchronization of a hyperchaotic Lorenz system is discussed using passive control. Based on the properties of a passive system, a passive controller is designed and the synchronization between two hyperchaotic Lorenz systems under different initial conditions is realized. Simulation results show the proposed synchronization method to be effective.展开更多
This paper investigates the control and synchronization of hyperchaotic Chen system based on the passive theory. By using two outputs, novel passive controllers are respectively designed to realize the globally asympt...This paper investigates the control and synchronization of hyperchaotic Chen system based on the passive theory. By using two outputs, novel passive controllers are respectively designed to realize the globally asymptotical stability of the hyperchaotic Chen system and the error dynamical system, which avoids mistakes in Ref.[11], where function W（z） cannot guarantee that fo（z） is globally asymptotically stable via only one output and W（z） is the Lyapunov function of f0（z）. Furthermore, numerical simulations are given to show the effectiveness of our method.展开更多
The aim of this paper is to introduce and investigate chaotic and hyperchaotic complex jerk equations. The jerk equations describe various phenomena in engineering and physics, for example, electrical circuits, laser ...The aim of this paper is to introduce and investigate chaotic and hyperchaotic complex jerk equations. The jerk equations describe various phenomena in engineering and physics, for example, electrical circuits, laser physics, mechanical oscillators, damped harmonic oscillators, and biological systems. Properties of these systems are studied and their Lyapunov exponents are calculated. The dynamics of these systems is rich in wide range of systems parameters. The control of chaotic attractors of the complex jerk equation is investigated. The Lyapunov exponents are calculated to show that the chaotic behavior is converted to regular behavior.展开更多
文摘The aim of this paper is to study the control of hyperchaofic complex nonlinear systems with unknown parameters using passive control theory. An approach is stated to design the passive controller and estimate the unknown parameters based on the property of the passive system. The feasibility and effectiveness of the proposed approach is demonstrated through its application to the hyperchaotic complex Lu system, as an example. The estimated values of the unknown parameters are calculated. The analytical form of the complex controller is derived and used in the numerical simulation to control the hyperchaotic attractors of this example. Block diagrams of this example using Matlab/Simulink are constructed after and before the control to ensure the validity of the analytical results. Other examples of hyperchaotic complex nonlinear systems can be similarly treated.
基金Project supported by the Natural Science Foundation of Fujian Province,China (Grant No.E0710018)
文摘This paper investigates the adaptive synchronization of hyperchaotic Lii systems based on the method of extended passive control. By combining the feedback control, the extended passive control method with two output variables is developed, which can synchronize hyperchaotic Lu systems asymptotically and globally more easily without knowing the bound of state of the hyperchaotic system. Adaptive laws are introduced to estimate the unknown parameters as well. Simulation results show the effectiveness and flexibility of the proposed control scheme.
文摘Synchronization of a hyperchaotic Lorenz system is discussed using passive control. Based on the properties of a passive system, a passive controller is designed and the synchronization between two hyperchaotic Lorenz systems under different initial conditions is realized. Simulation results show the proposed synchronization method to be effective.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60574045 and 70771084)
文摘This paper investigates the control and synchronization of hyperchaotic Chen system based on the passive theory. By using two outputs, novel passive controllers are respectively designed to realize the globally asymptotical stability of the hyperchaotic Chen system and the error dynamical system, which avoids mistakes in Ref.[11], where function W（z） cannot guarantee that fo（z） is globally asymptotically stable via only one output and W（z） is the Lyapunov function of f0（z）. Furthermore, numerical simulations are given to show the effectiveness of our method.
文摘The aim of this paper is to introduce and investigate chaotic and hyperchaotic complex jerk equations. The jerk equations describe various phenomena in engineering and physics, for example, electrical circuits, laser physics, mechanical oscillators, damped harmonic oscillators, and biological systems. Properties of these systems are studied and their Lyapunov exponents are calculated. The dynamics of these systems is rich in wide range of systems parameters. The control of chaotic attractors of the complex jerk equation is investigated. The Lyapunov exponents are calculated to show that the chaotic behavior is converted to regular behavior.
