Act-and-wait time-delayed feedback control of autonomous systems

Highlights: • Act-and-wait time-delayed feedback control algorithm is considered. • The algorithm is devised for autonomous single-input single-output systems. • An additional periodic small perturbation is introduced in the control law. • The theory for finding the required phase of the perturbation is developed. • The algorithm can stabilize periodic orbits with an odd number limitation property. - Abstract: Recently an act-and-wait modification of time-delayed feedback control has been proposed for the stabilization of unstable periodic orbits in nonautonomous dynamical systems (Pyragas and Pyragas, 2016 [30]). The modification implies a periodic switching of the feedback gain and makes the closed-loop system finite-dimensional. Here we extend this modification to autonomous systems. In order to keep constant the phase difference between the controlled orbit and the act-and-wait switching function an additional small-amplitude periodic perturbation is introduced. The algorithm can stabilize periodic orbits with an odd number of real unstable Floquet exponents using a simple single-input single-output constraint control.