A direct adaptive rapid tracking methodology for tracking complex traj
ectories in short-duration, linear, possibly slowly varying, and/or im
precisely known, industrial processes is proposed. The rapid tracking
is accomplished by injecting a supplemental control signal to the inpu
t of the plant. The direct adaptive control scheme adapts the stabiliz
ing controller to that which will yield fast convergence of the supple
mental control learning process. The complete controlled system is cap
able of tracking closely very complex short reference trajectories, ev
ert in the presence of plant input limitations (saturation).