  A new systematic approach to the construction of approximate solutions to a
class of nonlinear singularly perturbed feedback control systems using the
boundary layer functions especially with regard to the possible occurrence of
the boundary layers is proposed. For example, problems with feedback control,
such as the steady-states of the thermostats, where the controllers add or
remove heat, depending upon the temperature registered in another place of the
heated bar, can be interpreted with a second-order ordinary differential
equation subject to a nonlocal three--point boundary condition. The
$O(\epsilon)$ accurate approximation of behavior of these nonlinear systems in
terms of the exponentially small boundary layer functions is given. At the end
of this paper, we formulate the unsolved controllability problem for nonlinear
systems.
