Parameter Estimation in Adaptive Control of Time-Varying Systems Under a Range of Excitation Conditions

TL;DR

This paper introduces a novel adaptive control parameter estimation algorithm with time-varying learning rates that ensures rapid convergence of errors under excitation conditions, applicable to time-varying systems.

Contribution

It proposes a new algorithm with a matrix of time-varying learning rates that guarantees exponential convergence and boundedness without filtering regressor signals.

Findings

Guarantees global boundedness of state and parameter errors.

Ensures exponential convergence of errors under excitation conditions.

Provides theoretical bounds and numerical validation.

Abstract

This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error trajectories to tend exponentially fast towards a compact set whenever excitation conditions are satisfied. This algorithm is employed in a large class of problems where unknown parameters are present and are time-varying. It is shown that this algorithm guarantees global boundedness of the state and parameter errors of the system, and avoids an often used filtering approach for constructing key regressor signals. In addition, intervals of time over which these errors tend exponentially fast toward a compact set are provided, both in the presence of finite and persistent excitation. A projection operator is used to ensure the boundedness of the learning rate matrix, as compared to a time-varying forgetting factor. Numerical simulations are provided to complement the theoretical analysis.