Discrete-Time Adaptive Control of a Class of Nonlinear Systems Using High-Order Tuners

TL;DR

This paper introduces a novel adaptive control method for discrete-time nonlinear systems using high-order tuners, achieving stability and accelerated convergence by transforming the error model into an algebraic form.

Contribution

It applies high-order tuner algorithms to nonlinear system control, demonstrating stability and convergence through algebraic error model transformation.

Findings

Guaranteed bounded parameter estimation with time-varying regressors

Proven stabilization of nonlinear systems around reference trajectories

Accelerated convergence of tracking error with constant regressors

Abstract

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.