Act-and-wait time-delayed feedback control of nonautonomous systems.

Act-and-wait modification of a time-delayed feedback control (TDFC) algorithm is proposed to stabilize unstable periodic orbits in nonautonomous dynamical systems. Due to periodical switching on and off the control perturbation, an infinite-dimensional function space of the TDFC system is reduced to the finite-dimensional state space. As a result the number of Floquet exponents defining the stability of the controlled orbit remains the same as for the control-free system. The values of these exponents can be effectively manipulated by the variation of control parameters. We demonstrate the advantages of the modification for the chaotic nonautonomous Duffing oscillator with diagonal and nondiagonal control matrices. In both cases very deep minima of the spectral abscissa of Floquet exponents have been attained. The advantage of the modification is particularly remarkable for the nondiagonal coupling; in this case the conventional TDFC fails, whereas the modified version works.