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

摘要

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