  This paper presents an approach to target tracking that is based on a
variable-gain integrator and the Newton-Raphson method for finding zeros of a
function. Its underscoring idea is the determination of the feedback law by
measurements of the system's output and estimation of its future state via
lookahead simulation. The resulting feedback law is generally nonlinear. We
first apply the proposed approach to tracking a constant reference by the
output of nonlinear memoryless plants. Then we extend it in a number of
directions, including the tracking of time-varying reference signals by
dynamic, possibly unstable systems. The approach is new hence its analysis is
preliminary, and theoretical results are derived for nonlinear memoryless
plants and linear dynamic plants. However, the setting for the controller does
not require the plant-system to be either linear or stable, and this is
verified by simulation of an inverted pendulum tracking a time-varying signal.
We also demonstrate results of laboratory experiments of controlling a platoon
of mobile robots.
