Robustness of adaptive control augmentation of linear infinite dimensional systems using the kato gap metric

By Augmentation here we mean the addition of a nonlinear adaptive controller to a nominal infinite dimensional linear plant which is controlled by a linear infinite or finite dimensional baseline controller. In this paper we develop robustness results that accommodate two separate controllers: a baseline fixed gain controller to stabilize a possibly unstable nominal infinite dimensional plant and a nonlinear adaptive controller to augment the overall stability. Our results are based on the use of the gap metric which allows the stability robustness of the closed loop system to be assessed even when the plant is an unstable system. From the gap metric we generate a neighborhood of stability around a nominal infinite dimensional linear plant so that any other plant within this neighborhood will also be stabilized by the baseline controller. From this robustness result we develop a bound on the nonlinear adaptive controller so that it will maintain this robust stability, and in that sense “Do No Harm”.