$\mathcal {L}_1$ Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation (Hovakimyan, N. and Cao, C.; 2010 [Bookshelf]

TLDR: In this article, the authors describe a new method known as L1 adaptive control for bringing linear system design methods into adaptive control to confront several open problems, including the selection and tuning of adaptation gains, guaranteed transient performance of both states and controls, and guaranteed robustness margins.

Abstract: The book describes a new method known as L1 adaptive control for bringing linear system design methods into adaptive control to confront several open problems, including the selection and tuning of adaptation gains, guaranteed transient performance of both states and controls, and guaranteed robustness margins. Fast adaptation to allow aggressive maneuvering and recovery from failures is also confronted. A second key feature in L1 adaptive control is the use of a state-prediction system, whose dynamics can be prescribed and provide the reference model to be followed when the tracking and estimation errors are small. The third feature is the tuning of parameter estimates using projection methods. The block diagram of the resulting closed-loop adaptive system consists of linear components that can be analyzed using a mixture of linear frequency response techniques and adaptive control techniques.