Abstract and Applied Analysis
Volume 2009 (2009), Article ID 198353, 13 pages
doi:10.1155/2009/198353
A unified approach to high-gain adaptive controllers
Ian A. Gravagne1
, John M. Davis2
and Jeffrey J. Dacunha3
1Department of Electrical and Computer Engineering, Baylor University, Waco, TX 76798, USA
2Department of Mathematics, Baylor University, Waco, TX 76798, USA
3Spirit Global Energy Solutions, Midland, TX 79706, USA
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.