| 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 {dollar}Hsp{lcub}infty{rcub}{dollar} 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 presense of parametric uncertainty, unmodeled dynamics, and bounded noises is proved. This condition is based on the shifted {dollar}Hsp{lcub}infty{rcub}{dollar} norm of the frozen time system and is used as the underlying theoretical foundation of the {dollar}Hsp{lcub}infty{rcub}{dollar} robust adaptive controller. Numerical examples showing the effectiveness of the {dollar}Hsp{lcub}infty{rcub}{dollar} adaptive scheme are provided. |
