Discrete-time Indirect Adaptive Control for Systems with Disturbances via Directional Forgetting: Concurrent Learning Approach

TL;DR

This paper introduces a novel discrete-time adaptive control method for systems with disturbances that does not rely on persistent excitation or disturbance knowledge, ensuring stability and boundedness through directional forgetting and concurrent learning.

Contribution

It combines directional forgetting with concurrent learning to achieve adaptive control without persistent excitation or disturbance information, guaranteeing boundedness and improved stability.

Findings

Guarantees uniformly ultimately bounded (UUB) stability.

The ultimate bound can be designed via the forgetting factor.

The upper bound decreases over time, independent of system order.

Abstract

Recently, adaptive control systems with relaxed persistent excitation (PE) conditions have been proposed to guarantee true parameter convergence and improve the transient response. However, in some cases, sufficient control performance and parameter convergence cannot be easily achieved, with stability demonstrated only under ideal conditions, such as the absence of disturbances and matching conditions required. In this study, we propose a novel adaptive control method for discrete-time systems with disturbances, which is not under an ideal case, that combines directional forgetting and concurrent learning. The proposed method does not require the PE condition, information on disturbances, unknown parameters, or matching conditions, and it guarantees uniformly ultimately bounded (UUB). It was also theoretically demonstrated that the ultimate bound can be designed based on the forgetting factor, which is a design parameter. In addition, the upper bound decreases with time step, which is independent of the system order and/or target trajectory due to forgetting factor. This also implies stronger stability than a normal UUB. Numerical simulation results illustrate the effectiveness of the proposed method.