On Adaptive Control with Closed-loop Reference Models: Transients, Oscillations, and Peaking

TL;DR

This paper analyzes how Closed-loop Reference Models (CRMs) improve transient performance in adaptive control systems by reducing oscillations and peaking, providing bounds and optimal design strategies supported by simulations.

Contribution

It quantifies transient performance improvements with CRMs, derives bounds on parameter derivatives, and proposes an optimal CRM design to minimize peaking effects.

Findings

CRMs lead to smaller bounds on adaptive parameter derivatives.

Optimal CRM design reduces peaking phenomena.

Simulation results confirm theoretical improvements.

Abstract

One of the main features of adaptive systems is an oscillatory convergence that exacerbates with the speed of adaptation. Recently it has been shown that Closed-loop Reference Models (CRMs) can result in improved transient performance over their open-loop counterparts in model reference adaptive control. In this paper, we quantify both the transient performance in the classical adaptive systems and their improvement with CRMs. In addition to deriving bounds on L-2 norms of the derivatives of the adaptive parameters which are shown to be smaller, an optimal design of CRMs is proposed which minimizes an underlying peaking phenomenon. The analytical tools proposed are shown to be applicable for a range of adaptive control problems including direct control and composite control with observer feedback. The presence of CRMs in adaptive backstepping and adaptive robot control are also discussed. Simulation results are presented throughout the paper to support the theoretical derivations.