Symmetry and control: spatially extended chaotic systems

In a recent paper [Phys. Rev. E 57 (1998) 1550] it was demonstrated that the symmetries of the evolution equation and the target state have a profound effect on controlling the chaotic behavior. In the present paper we extend these results to the cases of time-periodic target trajectories and inexact symmetries, and apply the developed formalism to the problem of controlling spatiotemporal chaos. We use the example of a lattice dynamical system in arbitrary spatial dimension to show that there exists an intimate relationship between the geometry of an extended system and the geometry of feedback control.