Safe Adaptive Control: Data-Driven Stability Analysis and Robust Synthesis: 405 (Lecture Notes in Control and Information Sciences, 405) [Paperback] [Feb 10, 2011] Stefanovic, Margareta and Safonov, Michael G.

Safe Adaptive Control gives a formal and complete algorithm for assuring the stability of a switched control system when at least one of the available candidate controllers is stabilizing. The possibility of having an unstable switched system even in the presence of a stabilizing candidate controller is demonstrated by referring to several well-known adaptive control approaches, where the system goes unstable when a large mismatch between the unknown plant and the available models exists ("plant-model mismatch instability"). Sufficient conditions for this possibility to be avoided are formulated, and a "recipe" to be followed by the control system designer to guarantee stability and desired performance is provided. The problem is placed in a standard optimization setting. Unlike the finite controller sets considered elsewhere, the candidate controller set is allowed to be continuously parametrized so that it can deal with plants with a very large range of uncertainties.

From the reviews:

“The authors start with a subjective ‘overview of adaptive control’ and ‘literature review’ ... underlying the limitations of the existing adaptive control algorithms and motivating the concepts presented in the book. ... Safe adaptive control by Stefanovic and Safonov may be recommended to any control engineer active in the adaptive control field.” (Jacek Kabziński, Mathematical Reviews, Issue 2012 b)