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Transient and Asymptotic Properties of Robust Adaptive Controllers in the Presence of Non-Coercive Lyapunov Functions
Journal
Proceedings of the IEEE Conference on Decision and Control
ISSN
07431546
Date Issued
2021-01-01
Author(s)
Paranjape, Aditya A.
Natarajan, Vivek
Ghosh, Supratim
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 {{mathcal{L}}_1} 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.