This paper concerns the adaptive control of a class of discrete-time
nonlinear systems with all states accessible. Recently, a high-order tuner
algorithm was developed for the minimization of convex loss functions with
time-varying regressors in the context of an identification problem. Based on
Nesterov's algorithm, the high-order tuner was shown to guarantee bounded
parameter estimation when regressors vary with time, and to lead to accelerated
convergence of the tracking error when regressors are constant. In this paper,
we apply the high-order tuner to the adaptive control of a particular class of
discrete-time nonlinear dynamical systems. First, we show that for plants of
this class, the underlying dynamical error model can be causally converted to
an algebraic error model. Second, we show that using this algebraic error
model, the high-order tuner can be applied to provably stabilize the class of
dynamical systems around a reference trajectory.Comment: 8 pages, submitted to the 2023 AC