Accelerated Performance and Accelerated Learning with Discrete-Time High-Order Tuners

TL;DR

This paper analyzes two high-order tuners inspired by advanced optimization methods, demonstrating their exponential convergence and superior performance in parameter estimation compared to normalized gradient descent.

Contribution

It introduces and analyzes two high-order tuners based on Polyak's heavy ball and Nesterov's methods, showing their accelerated convergence properties.

Findings

Parameter estimates are bounded and converge exponentially fast.

Simulation confirms superior performance over normalized gradient descent.

Effective in scenarios with persistently exciting regressors.

Abstract

We consider two high-order tuners that have been shown to have accelerated performance, one based on Polyak's heavy ball method and another based on Nesterov's acceleration method. We show that parameter estimates are bounded and converge to the true values exponentially fast when the regressors are persistently exciting. Simulation results corroborate the accelerated performance and accelerated learning properties of these high-order tuners in comparison to algorithms based on normalized gradient descent.