Time-optimal chaos control by center manifold targeting.
Ott-Grebogi-Yorke control and its map-based variants work by targeting the (linear) stable subspace of the target orbit so that after one application of the control the system will be in this subspace. I propose an n-step variation, where n is the dimension of the system, that sends any initial condition in a controllable region directly to the target orbit instead of its stable subspace. This method is time optimal, in that, up to modeling and measurement error, the system is completely controlled after n iterations of the control procedure. I demonstrate the procedure using a piecewise linear and a nonlinear two-dimensional map, and indicate how the technique may be extended to maps and flows of higher dimension.
Starrett
John
J
Department of Mathematics, University of Colorado, 3500 Clay Street, Denver 80211, USA.