LINEAR AND OPTIMAL NONLINEAR CONTROL OF ONE-DIMENSIONAL MAPS

We investigate the effects of linear and optimal non-linear control in the simple case of one-dimensional unimodal maps. We show that linear feedback relates unimodal maps to invertible ''Henon-like'' maps. Thi s observation should be useful in relating the considerable bodies of knowledge which exist far the two types of systems. in the case of the optimal non-linear feedback scheme of de Sousa Vieira and Lichtenberg we investigate the relationship between controlled and uncontrolled m aps, particularly the preservation of the period doubling route to cha os. (C) 1997 Elsevier Science B.V.