From Adaptive Differential Games to Disturbance-Robust Adaptive Control

Abstract The title of this semi-tutorial, expository paper might be applicable to the remarkable body of research by Professor Tamer Başar with his students Didinski and Pan in the 1990s on robustification of parameter identifiers and adaptive controllers through game-theoretic methods. The author’s inspiration indeed fuses their work with his results from that period on inverse optimal adaptive stabilization and inverse optimal disturbance attenuation in a differential game formulation. Inverse optimal adaptive and minimax techniques are merged in this paper’s first half to obtain solutions to adaptive differential games between the adaptive controller and a disturbance. The article’s second half introduces a recent advance in disturbance-robustification of adaptive control for persistent disturbances (merely bounded, rather than square-integrable), by Iasson Karafyllis and this article’s author. While not with a minimax capability, this robustification is first in forty years to attain regulation with a bias that is arbitrarily low and independent of both the unknown parameter and the persistent disturbance.