  In this work, we establish a convenient similarity between an adaptive
backstepping control law and a standard proportional-integral-derivative (PID)
controller for a class of second-order systems. The extracted similarity
provides a deeper understanding of the adaptive backstepping design from a
performance perspective via an intuitive method to select its otherwise
abstract controller gains, on top of its traditional stability perspective.
Such a similarity analysis opens the door for researchers to use
well-established PID tuning methods to predict the performance of Lyapunov
stability-based controllers. At the same time, the obtained formulation reveals
how the corresponding PID control law can be linked to Lyapunov stability
theory.
