Global Stability Notions to Enhance the Rigor and Robustness of Adaptive Control

TL;DR

This paper discusses advanced global stability concepts essential for the development and analysis of adaptive control systems, emphasizing their mathematical foundations and relevance for time-invariant systems.

Contribution

It introduces and explains global stability notions specific to adaptive control, enhancing the theoretical rigor and robustness analysis in this field.

Findings

Clarifies the role of global stability in adaptive control

Develops mathematical tools for stability proofs

Highlights the importance of stability notions in adaptive control

Abstract

Stability theory plays a crucial role in feedback control. However, adaptive control theory requires advanced and specialized stability notions that are not frequently used in standard feedback control theory. The present document is a set of notes for a graduate course. It describes the global stability notions needed in (robust) adaptive control and develops the mathematical tools that are used for the proof of such stability properties. Moreover, the document shows why and how these global stability properties arise in adaptive control. We focus on stability properties for time-invariant systems. Consequently, tracking control problems are not covered by the present document.