Controlling chaos to unstable periodic orbits and equilibrium state solutions for the coupled dynamos system

In the case where the knowledge of goal states is not known, the controllers are constructed to stabilize unstable steady states for a coupled dynamos system. A delayed feedback control technique is used to suppress chaos to unstable focuses and unstable periodic orbits. To overcome the topological limitation that the saddle-type steady state cannot be stabilized, an adaptive control based on LaSalle＇s invariance principle is used to control chaos to unstable equilibrium （i.e. saddle point, focus, node, etc.）. The control technique does not require any computer analysis of the system dynamics, and it operates without needing to know any explicit knowledge of the desired steady-state position.

Controlling chaos using Takagi-Sugeno fuzzy model and adaptive adjustment

In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno （TS） fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control from Lyapunov stability theory. The proposed approach offers a systematic design procedure for stabilizing a large class of chaotic systems in the literature about chaos research. The simulation results on Rossler＇s system verify the effectiveness of the proposed methods.

Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.

Controlling chaos in RCL-shunted Josephson junction by delayed linear feedback

The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.

Controlling chaos in power system based on finite-time stability theory

Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.

Pole placement method of controlling chaos in DC-DC buck converters

Based on the mechanism for the generation of chaos in a buck converter, a pole placement method is proposed and applied to controlling the chaos in a circuit. The control circuit is designed and tested. Numerical calculation and circuit implementation demonstrate the validity of this chaos control method.

Controlling Chaos in Neuron Based on Lasalle Invariance Principle

A new control law is proposed to asymptotically stabilize the chaotic neuron system based on LaSalleinvariant principle.The control technique does not require analytical knowledge of the system dynamics and operateswithout an explicit knowledge of the desired steady-state position.The well-known modified Hodgkin-Huxley (MHH)and Hindmarsh-Rose (HR) model neurons are taken as examples to verify the implementation of our method.Simulationresults show the proposed control law is effective.The outcome of this study is significant since it is helpful to understandthe learning process of a human brain towards the information processing,memory and abnormal discharge of the brainneurons.

Controlling beam halo-chaos via backstepping design

A backstepping control method is proposed for controlling beam halo-chaos in the periodic focusing channels （PFCs） of high-current ion accelerator. The analysis and numerical results show that the method, via adjusting an exterior magnetic field, is effective to control beam halo chaos with five types of initial distribution ion beams, all statistical quantities of the beam halo-chaos are largely reduced, and the uniformity of ion beam is improved. This control method has an important value of application, for the exterior magnetic field can be easily adjusted in the periodical magnetic focusing channels in experiment.

CONTROLLING HYPERCHAOS IN PLANAR SYSTEMS BY ADJUSTING PARAMETERS

For the two_parameter family of planar mapping, a method to stabilize an unstable fixed point without stable manifold embedding in hyperchaos is introduced. It works by adjusting the two parameters in each iteration of the map. The explicit expressions for the parameter adjustments are derived, and strict proof of convergence for method is given.

Phase Effect in Controlling Non-autonomous Chaos in the Presence of Noise

The effect of random phase on the Josephson junction system dynamic model is investigated.It is shown that random phase has the suppressing ability for controlling chaos.The top Lyapunov exponent is used to detect the chaotic dynamics in the system,and the method for calculating the top Lyapunov exponent is based on Khasminskii’s spherical coordinate formulation for linear stochastic systems.In addition,Poincarémap,phase portraits and time evolution are investigated to verify the obtained results.It is found that these results have the excellent agreement.

MODEL FOR CHAOS CONTROL OF REGIONAL Ec-R-Ev SYSTEM

In order to realize the coordination oriented management of the economy resource environment(Ec R Ev) composite system,its optimal aggregate coordinating measurement model is established.A self learning method is presented,which combines the optimizing technology and stability analysis together to achieve a tradeoff between the optimizing objective and system stability.So a model for chaos control of the composite system based on coordination is proposed.

Controlling Chaotic Behavior in a Bose-Einstein Condensate with Linear Feedback

The spatial structure of a Bose-Einstein condensate （BEC） loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative.

CONTROLLING CHAOTIC OSCILLATIONS OF VISCO-ELASTIC PLATESBY THE LINEARIZATION VIA OUTPUTFEEDBACK

Controlling chaotic oscillations of viscoelastic plates are investigated in this paper. Based on the exact linearization method in nonlinear system control theory, a nonlinear feedback control law is presented for a class of non_affine control systems. The mathematical model describing motion of nonlinear viscoelastic plates is established, and it is simplified by the Galerkin method. The phase space portrait and the power spectrum are employed to demonstrate chaos in the system. The deflection is treated as an output, and is controlled to given periodic goals.

Controlling Chaotic Cscillations with Input-Output Linearization

In this paper, the nonlinear control of chaotic oscillations was investigated by using the input output linearization control method. The chaotic attitude of a kind of spacecraft was discussed. It is demonstrated that the input output linearization control law is the nonlinear version of the parametric open plus closed loop control law.

Fuzzy Chaos Control for Vehicle Lateral Dynamics Based on Active Suspension System

The existing research of the active suspension system（ASS） mainly focuses on the different evaluation indexes and control strategies. Among the different components, the nonlinear characteristics of practical systems and control are usually not considered for vehicle lateral dynamics. But the vehicle model has some shortages on tyre model with side-slip angle, road adhesion coefficient, vertical load and velocity. In this paper, the nonlinear dynamic model of lateral system is considered and also the adaptive neural network of tire is introduced. By nonlinear analysis methods, such as the bifurcation diagram and Lyapunov exponent, it has shown that the lateral dynamics exhibits complicated motions with the forward speed. Then, a fuzzy control method is applied to the lateral system aiming to convert chaos into periodic motion using the linear-state feedback of an available lateral force with changing tire load. Finally, the rapid control prototyping is built to conduct the real vehicle test. By comparison of time response diagram, phase portraits and Lyapunov exponents at different work conditions, the results on step input and S-shaped road indicate that the slip angle and yaw velocity of lateral dynamics enter into stable domain and the results of test are consistent to the simulation and verified the correctness of simulation. And the Lyapunov exponents of the closed-loop system are becoming from positive to negative. This research proposes a fuzzy control method which has sufficient suppress chaotic motions as an effective active suspension system.

Chaos Control in a New Three-Dimensional Chaotic T System

In this paper, we study chaos control of the new 3D chaotic system. We use three feedback methods （the linear, speed, doubly-periodic function controller） to suppress the chaos to unstable equilibrium. As a result, some controllers are obtained. Moreover, numerical simulations are used to verify the effectiveness of the obtained controllers.

Passive adaptive control of chaos in synchronous reluctance motor

The performance of synchronous reluctance motor （SynRM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in SynRM, a passive control law is presented in this paper, which transforms the chaotic SynRM into an equivalent passive system. It is proved that the equivalent system can be asymptotically stabilized at the set equilibrium point, namely, chaos in SynRM can be controlled. Moreover, in order to eliminate the influence of undeterministic parameters, an adaptive law is introduced into the designed controller. Computer simulation results show that the proposed controller is very effective and robust against the uncertainties in systemic parameters. The present study may help to maintain the secure operation of industrial servo drive system.

A survey on delayed feedback control of chaos

This paper introduces the basic idea and provides the mathematical formulation of the delayed feedback control （DFC） methodology, which has been widely used in chaos control. Stability analysis including the well-known odd number linfitation of the DFC is reviewed. Some new developments in characterizing the limitation of the DFC are presented. Various modified DFC methods, which are developed in order to overcome the odd number limitation, are also described. Finally, some open problems in this research field are discussed.

Hybrid control of bifurcation and chaos in stroboscopic model of Internet congestion control system

Interaction between transmission control protocol （TCP） and random early detection （RED） gateway in the Internet congestion control system has been modelled as a discrete-time dynamic system which exhibits complex bifurcating and chaotic behaviours. In this paper, a hybrid control strategy using both state feedback and parameter perturbation is employed to control the bifurcation and stabilize the chaotic orbits embedded in this discrete-time dynamic system of TCP/RED. Theoretical analysis and numerical simulations show that the bifurcation is delayed and the chaotic orbits are stabilized to a fixed point, which reliably achieves a stable average queue size in an extended range of parameters and even completely eliminates the chaotic behaviour in a particular range of parameters. Therefore it is possible to decrease the sensitivity of RED to parameters. By using the hybrid strategy, we may improve the stability and performance of TCP/RED congestion control system significantly.

Notch filter feedback controlled chaos in buck converter

A method of controlling chaos in the voltage-mode buck converter is presented by using an improved notch filter feedback control in this paper. The proposed control part comprises a notch filter and a low-pass filter. The discrepancy between the outputs of the two filters is introduced into the control prototype of the power converter. In this way, the system period-1 solution is kept unchanged. The harmonic balance method is applied to analysing the variation law of the system bifurcation point, and then the stable range of the feedback gain is ascertained. The results of simulation and experiment are also given finally.