  We generalize a method of control of chaos which uses delayed feedback at the
period of an unstable orbit to stabilize that orbit. The generalization
consists of substituting some portion of the nonlinear dynamical system with a
delayed dynamics, rather than using a linear delay function for control. A
further generalization, in which the control function retains memory of all
previous periods, allows the region of the parameter space over which control
can be achieved to be extended, but at the price of losing the ability to
achieve superstability. Nonliner feedback results in a larger basin of
attraction to the stabilized orbit than linear feedback. For a simple test
mapping studied (the logistic map) the dimension of the system increases from
one to two by introducing control. We show in the case involving memory, for a
particular choice of the relationship between the control parameters, that the
superstable orbit can be recovered without reducing the parameter space that
can be controlled. This particular solution, in addition to having the largest
basin of attraction of the methods considered, retains the dimension of the
uncontrolled system.
