Stabilization of chaotic systems via act-and-wait delayed feedback control using a high-precision direct integration method

A technique for the numerical analysis of the stability problem in chaotic systems via act-and-wait delayed feedback control is developed and justified. Recently, act-and-wait modification of a delayed feedback control method is proposed to stabilize unstable periodic orbits in dynamical systems. To overcome the difficulties in obtaining conditions under which the state of closed-loop system converges toward a periodic solution via the act-and-wait scheme, this paper presents a high-precision direct integration method for calculating the monodromy matrix corresponding to the closed-loop system based on the theory of Peano–Baker series. The capabilities of the proposed schemes in stabilization of unstable periodic orbits of chaotic systems are illustrated by numerical examples.