Converting chaos into periodic motion by state feedback control

A simple control method is presented to convert chaos into periodic motion by using linear state feedback of an available system variable. The low-periodic orbits can be derived from the chaotic attractor with slight change of the dynamical structure in the original dynamics. Melnikov's perturbation method in generalized Hamiltonian systems is introduced to explain the control mechanism of directing chaotic motion towards low-periodic motion in the Lorenz equations. Moreover, the existence of periodic orbits is examined in the perturbed Lorenz system. Simulation results verify the effectiveness of Melnikov's analysis.