Design and robustness of delayed feedback controllers for discrete systems

Control of electrical alternans in simulations of paced myocardium using extended time-delay autosynchronization

Experimental studies have linked alternans, an abnormal beat-to-beat alternation of cardiac action potential duration, to the genesis of lethal arrhythmias such as ventricular fibrillation. Prior studies have considered various closed-loop feedback control algorithms for perturbing interstimulus intervals in such a way that alternans is suppressed. However, some experimental cases are restricted in that the controller's stimuli must preempt those of the existing waves that are propagating in the tissue, and therefore only shortening perturbations to the underlying pacing are allowed. We present results demonstrating that a technique known as extended time-delay autosynchronization (ETDAS) can effectively control alternans locally while operating within the above constraints. We show that ETDAS, which has already been used to control chaos in physical systems, has numerous advantages over previously proposed alternans control schemes.

Conversion of stability in systems close to a Hopf bifurcation by time-delayed coupling

We propose a control method with time delayed coupling which makes it possible to convert the stability features of systems close to a Hopf bifurcation. We consider two delay-coupled normal forms for Hopf bifurcation and demonstrate the conversion of stability, i.e., an interchange between the sub- and supercritical Hopf bifurcation. The control system provides us with an unified method for stabilizing both the unstable periodic orbit and the unstable steady state and reveals typical effects like amplitude death and phase locking. The main method and the results are applicable to a wide class of systems showing Hopf bifurcations, for example, the Van der Pol oscillator. The analytical theory is supported by numerical simulations of two delay-coupled Van der Pol oscillators, which show good agreement with the theory.

Control of unstable steady states by long delay feedback

We present an asymptotic analysis of time-delayed feedback control of steady states for large delay time. By scaling arguments, and a detailed comparison with exact solutions, we establish the parameter ranges for successful stabilization of an unstable fixed point of focus type. Insight into the control mechanism is gained by analyzing the eigenvalue spectrum, which consists of a pseudocontinuous spectrum and up to two strongly unstable eigenvalues. Although the standard control scheme generally fails for large delay, we find that if the uncontrolled system is sufficiently close to its instability threshold, control does work even for relatively large delay times.

Controlling drift-wave turbulence using time-delay and space-shift autosynchronization feedback

Drift-wave turbulence control in a one-dimensional nonlinear drift-wave equation driven by a sinusoidal wave is considered. We apply time-delay and space-shift feedback signals, to suppress turbulence. By using global and local pinning strategies, we show numerically that the turbulent state can be controlled to periodic states effectively if appropriate time-delay length and space-shift distance are chosen. The physical mechanism of the control scheme is understood based on the energy-minimum principle.

Control of unstable steady states by time-delayed feedback methods

We show that time-delayed feedback methods, which have successfully been used to control unstable periodic orbits, provide a tool to stabilize unstable steady states. We present an analytical investigation of the feedback scheme using the Lambert function and discuss effects of both a low-pass filter included in the control loop and nonzero latency times associated with the generation and injection of the feedback signal.