A Unified Approach to High-Gain Adaptive Controllers. (24th January 2010)

• Record Type: Journal Article
• Authors: Gravagne, Ian A.; Davis, John M.; DaCunha, Jeffrey J.
• Other Names: Peterson Allan C. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2009(2009)
• Publication Date: 2010-01-24
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2009/198353
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : It has been known for some time that proportional output feedback will stabilize MIMO, minimum-phase, linear time-invariant systems if the feedback gain is sufficiently large. High-gain adaptive controllers achieve stability by automatically driving up the feedback gain monotonically. More recently, it was demonstrated that sample-and-hold implementations of the high-gain adaptive controller also require adaptation of the sampling rate. In this paper, we use recent advances in the mathematical field of dynamic equations on time scales to unify and generalize the discrete and continuous versions of the high-gain adaptive controller. We prove the stability of high-gain adaptive controllers on a wide class of time scales.