H_infinity Robust Adaptive Control

Abstract

Traditional adaptive control algorithms are not robust to dynamic uncertainties. The robust adaptive control algorithms developed previously to deal with dynamic uncertainties do not facilitate quantitative design to predefined robustness specifications. Their design procedures require time-consuming trial-and-error. We proposed a new robust adaptive control algorithm with a systematic and quantitative design procedure. The adaptive controller consists of an H_infinity suboptimal control law and a robust parameter estimator. Stability and robustness analysis is based on a general frozen time analysis framework. Global boundedness of the adaptive control system in the presence of parametric uncertainty, unmodeled dynamics, and bounded noises is proved. This condition is based on the shifted H_infinity norm of the frozen time system and is used as the underlying theoretical foundation of the H_infinity robust adaptive controller. Numerical examples showing the effectiveness of the H_infinity adaptive scheme are provided.