Control of Unstable Periodic Orbit by Means of Projective Operator Method

We define the projective operators for controlling unstable periodic orbit(UPO), and project the eigenvectors of Jacobian matrix of a system in the direction of trajectory and in the direction perpendicular to the trajectory. Then the two eigenvalues in the perpendicular direction are changed to negative ones by adjusting the controlling parameter. So the control of UPO can be implemented. It is also shown that the procedure is effective even in the presence of noise.