Adaptive delayed feedback control for stabilizing unstable steady states

Abstract

Delayed feedback control is a commonly used control method for stabilizing unstable periodic orbits and unstable steady states. The present paper proposes an adaptive tuning delay time rule for delayed feedback control focused on stabilizing unstable steady states. The rule is designed to slowly vary the delay time, increasing the difference between the past and current states of dynamical systems, which induces the delay time to automatically fall into the stability region. We numerically confirm that the tuning rule works well for the Stuart–Landau oscillator, FitzHugh–Nagumo model, and Lorenz system.