Transient and Asymptotic Properties of Robust Adaptive Controllers in the Presence of Non-Coercive Lyapunov Functions

TL;DR

This paper investigates how the lack of coercive Lyapunov functions affects the performance and robustness of adaptive control systems, especially those using parameter observers like L1 adaptive architecture.

Contribution

It provides an analysis of the impact of non-coercive Lyapunov functions on the bounds, performance, and robustness of adaptive controllers.

Findings

Non-coercive Lyapunov functions can limit analytical bounds.

Performance and robustness are affected by the non-existence of coercive Lyapunov operators.

Implications for the design of adaptive controllers using Lyapunov methods.

Abstract

Adaptive control architectures often make use of Lyapunov functions to design adaptive laws. We are specifically interested in adaptive control methods, such as the well-known L1 adaptive architecture, which employ a parameter observer for this purpose. In such architectures, the observation error plays a critical role in determining analytical bounds on the tracking error as well as robustness. In this paper, we show how the non-existence of coercive Lyapunov operators can impact the analytical bounds, and with it the performance and the robustness of such adaptive systems.