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. (C) 2000 Elsevier Science B.V. All rights reserved.