Time-delayed Feedback Control Method Research Articles

Chaos control applied to cardiac rhythms represented by ECG signals

The control of irregular or chaotic heartbeats is a key issue in cardiology. In this regard, chaos control techniques represent a good alternative since they suggest treatments different from those traditionally used. This paper deals with the application of the extended time-delayed feedback control method to stabilize pathological chaotic heart rhythms. Electrocardiogram (ECG) signals are employed to represent the cardiovascular behavior. A mathematical model is employed to generate ECG signals using three modified Van der Pol oscillators connected with time delay couplings. This model provides results that qualitatively capture the general behavior of the heart. Controlled ECG signals show the ability of the strategy either to control or to suppress the chaotic heart dynamics generating less-critical behaviors.

Chaos Control of a Chemical Chaotic System via Time-delayed Feedback Control Method

In this paper, the control of chemical chaotic dynamical system is investigated by time-delayed feedback control technique. The controllability and the stability of the equilibriums and local Hopf bifurcation of the system are verified. Some numerical simulations which show the effectiveness of the time-delayed feedback control method are provided.

Adaptive search for the optimal feedback gain of time-delayed feedback controlled systems in the presence of noise

We propose two adaptive algorithms for the time-delayed feedback control method to tune the feedback gain to an optimal value in the presence of noise. By the optimal value we mean the value of the feedback gain that minimizes the mean square of the control signal. The first algorithm is model independent; it uses trial values of the feedback gain and defines the optimal value by the least-squares polynomial fitting. The second algorithm is based on the gradient descent method and requires the knowledge of the system equations. Here any initial value of the feedback gain is continuously adjusted towards the optimal value without any trials. The efficacy of the algorithms is demonstrated with different specific models, namely, a simple linear map, the Rossler system and the normal form of the subcritical Hopf bifurcation.

Experimental time-delayed feedback control with variable and distributed delays

We report on several improvements of the classical time-delayed feedback control method for stabilization of unstable periodic orbits or steady states. In an electronic circuit experiment, we were able to realize time-varying and distributed delays in the control force leading to successful control for large parameter sets, including large time delays. The presented techniques make advanced use of the natural torsion of the orbits, which is also necessary for the original control method to work.

BIFURCATION CONTROL OF A PARAMETRIC PENDULUM

In this paper, we apply chaos control methods to modify bifurcations in a parametric pendulum-shaker system. Specifically, the extended time-delayed feedback control method is employed to maintain stable rotational solutions of the system avoiding period doubling bifurcation and bifurcation to chaos. First, the classical chaos control is realized, where some unstable periodic orbits embedded in chaotic attractor are stabilized. Then period doubling bifurcation is prevented in order to extend the frequency range where a period-1 rotating orbit is observed. Finally, bifurcation to chaos is avoided and a stable rotating solution is obtained. In all cases, the continuous method is used for successive control. The bifurcation control method proposed here allows the system to maintain the desired rotational solutions over an extended range of excitation frequency and amplitude.

Hopf bifurcation control in the XCP for the Internet congestion control system

In this paper, we investigated the Hopf bifurcation of the e Xplicit Control Protocol (XCP) for the Internet congestion control system. These bifurcation behaviors may cause heavy oscillation of average queue length and induce network instability. A time-delayed feedback control method was proposed for controlling Hopf bifurcation in the XCP system. Numerical simulation results are presented to show that the time-delayed feedback controller is efficient in controlling Hopf bifurcation.

Stabilizing the Average-Current-Mode-Controlled Boost PFC Converter via Washout-Filter-Aided Method

The average-current-mode-controlled boost power-factor-correction (PFC) converter may exhibit instability at the line frequency. This nonlinear phenomenon is undesirable. The time-delay feedback control method may stabilize the boost PFC converter by introducing a digital circuit. The digital circuit is difficult to implement. The second-order filter method can also control the instability, but its implementation is a little complex. In this brief, the washout-filter-aided method is proposed to stabilize the boost PFC converter. The dynamic-phasor-based harmonic averaged model of the converter is derived by applying the harmonic balance method to the averaged model. The equilibrium point of the first-order harmonic model is the origin. This equilibrium point may be stabilized by appropriately choosing the parameters of the washout filter so as to stabilize the PFC converter. Numerical simulation verifies the effectiveness of the washout-filter-aided method.

Chaos control applied to heart rhythm dynamics

The dynamics of cardiovascular rhythms have been widely studied due to the key aspects of the heart in the physiology of living beings. Cardiac rhythms can be either periodic or chaotic, being respectively related to normal and pathological physiological functioning. In this regard, chaos control methods may be useful to promote the stabilization of unstable periodic orbits using small perturbations. In this article, the extended time-delayed feedback control method is applied to a natural cardiac pacemaker described by a mathematical model. The model consists of a modified Van der Pol equation that reproduces the behavior of this pacemaker. Results show the ability of the chaos control strategy to control the system response performing either the stabilization of unstable periodic orbits or the suppression of chaotic response, avoiding behaviors associated with critical cardiac pathologies.

Stability and time-delayed feedback control of a relative-rotation nonlinear dynamical system under quasic-periodic parametric excitation

The dynamical equation of a relative-rotation nonlinear dynamic system, which contains quasi-periodic parametric excitation and time delays, is established. Bifurcation response equation of 1/2 subharmonic primary parametric resonance is obtained by the method of multiple scales, and the stability of the system is analyzed. By solving the steady state solutions of the uncontrolled system, the effect of quasi-periodic parametric excitation on system response is studied through discussing the dynamics of the system. Time-delay feedback control method is used to control the bifurcation and limit cycle(region). Numerical results show that the bifurcation and the stability of the limit cycle(region) are controlled effectively by changing the time-delay parameters.

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.

Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method

Chaos control is employed for the stabilization of unstable periodic orbits (UPOs) embedded in chaotic attractors. The extended time-delayed feedback control uses a continuous feedback loop incorporating information from previous states of the system in order to stabilize unstable orbits. This article deals with the chaos control of a nonlinear pendulum employing the extended time-delayed feedback control method. The control law leads to delay-differential equations (DDEs) that contain derivatives that depend on the solution of previous time instants. A fourth-order Runge–Kutta method with linear interpolation on the delayed variables is employed for numerical simulations of the DDEs and its initial function is estimated by a Taylor series expansion. During the learning stage, the UPOs are identified by the close-return method and control parameters are chosen for each desired UPO by defining situations where the largest Lyapunov exponent becomes negative. Analyses of a nonlinear pendulum are carried out by considering signals that are generated by numerical integration of the mathematical model using experimentally identified parameters. Results show the capability of the control procedure to stabilize UPOs of the dynamical system, highlighting some difficulties to achieve the stabilization of the desired orbit.

On a new time-delayed feedback control of chaotic systems

In this paper, using the idea of the successive dislocation feedback method, a new time-delayed feedback control method called the successive dislocation time-delayed feedback control (SDTDFC) is designed. Firstly, the idea of SDTDFC is introduced. Then some analytic sufficient conditions of the chaos control from the SDTDFC approach are derived for stabilization. Finally, some established results are further clarified via a case study of the Lorenz system with the numerical simulations.

Eliminating oscillations in the Internet by time-delayed feedback control

In this paper, a time-delayed feedback control method is applied to congestion control in order to eliminate oscillations in the Internet. The stability of the proposed control method is demonstrated based on frequency-domain analysis. The effectiveness of the method is illustrated using simulation.

Control of microcantilevers in dynamic force microscopy using time delayed feedback

It has been recently shown that microcantilever sensors in dynamic force microscopes possibly exhibit chaotic oscillations due to the nonlinear tip-sample interaction force. In this article, we propose elimination of the chaotic oscillations using the time delayed feedback control method, which has an ability to stabilize unstable periodic orbits embedded in chaotic attractors. An extended operating range of the microscopes is numerically estimated by stability analysis of the target periodic oscillation. We also discuss an improved transient response of oscillation, which allows us to accelerate the scanning rate of the microscopes without reducing their force sensitivity.

Controlling Symmetry Breaking in Periodically Driven Bistable System: Preliminary Consideration

A time-delayed feedback control method to stabilize an unstable symmetric orbit under broken symmetric regime in a periodically driven bistable system is proposed. Basic idea of the method or its physical meaning is introduced via simplified model controlled system. Its improved ability on the stabilization compared to the conventional method is shown by some numerical evidences.

Bifurcation analysis and control in Turbo decoding algorithm

Turbo Codes can approach the Shannon limit very closely with the help of its special iterative decoding algorithm. This paper establishes a nonlinear dynamic system to analyze the relationship between Turbo decoding output and the number of iterations. Here, the number of iterations is taken as the time axis, decoding output as the state variable, SNR and information bits N as system parameters. It is shown that with SNR increasing, the decoding algorithm undergoes three stages, namely the indecisive fix-point, singular region and unequivocal fix-point. Bifurcations occur during the transformation from the indecisive fix-point to the singular region. It is first proposed that fold, period doubling and Neimark-Sacker bifurcation all have the possibility to occur, depending on the value of N. In the singular region, phase trajectories may appear as period-two, period-three, quasiperiod and chaos. This paper first observed and confirmed the existence of period-three and chaos. Singular region deteriorates the performance of Turbo codes under low SNR. This paper proposes a time-delay feedback control method to stablize the fix-point. Simulation results show that this method achieves 0.1—0.3 dB improvement for Turbo codes under low SNR condition.

Time-Delayed Feedback Control Method for Dynamical Symmetry Breaking in a Periodically Driven Bistable System

(Received August 7, 2005) With the aim of formulating a method to control dynamic phase transitions in periodically driven bistable systems with reversal symmetry, a time-delayed feedback control method to stabilize an unstable periodic orbit in the broken symmetric regime is studied. In order to overcome a limitation of the conventional time-delayed feedback method, another extended scheme is proposed, and its improved ability with respect to stabilization is proved. Through the linear stability analysis of model controlled systems driven by sinusoidal fields, basic differences between the conventional and proposed methods are extracted. It is clarified that a few characteristics around the bifurcation point from the pitchfork critical branch to the Hopf branch and the turning point of the Hopf critical branch classify essential features of the stability diagram and concern restrictions for stabilization. Within the linear stability treatment, this paper estimates a safe choice and an effective range of feedback gains in the proposed method.

Controlling Beam Halo-Chaos via Time-Delayed Feedback**The project supported by National Natural Science Foundation of China under Grant Nos. 10247005, 70071047, and 19875080

The study of controlling high-current proton beam halo-chaos has become a key concerned issue for many important applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Particle in cell simulation results show that the method is very effective and has some advantages for high-current beam experiments and engineering.

Control of chaos in a PWM current-mode H-bridge inverter using time-delayed feedback

Time-delayed feedback can be used to stabilize unstable periodic orbits (UPOs) in dynamical systems. The technique involves feedback of signals delayed by the orbit's period so that the feedback signals vanish on the target orbit and hence the UPO becomes a solution of the original system. An obvious advantage of this method is that it requires only the knowledge of the period of the target UPO. In this brief, a pulsewidth-modulated current-mode H-bridge inverter serves as a subject of investigation. Under certain parameter ranges, it exhibits higher periodic solutions and chaos. A simple time-delay feedback control method is applied to stabilize the UPOs. By using the time-delayed feedback control method, the stability limit and gain range of the system are increased.