L1 Adaptive Control for Systems with Integral Feedback Augmentation

L₁ adaptive control is a new adaptive control methodology developed in recent years with good robustness properties and some distinguishing features, such as fast adaptation and guaranteed transient closed-loop response. However, the L₁ adaptive control architecture in various forms in currently available literature has not considered systems with integrated output tracking error as augmented states. This paper extends the L₁ adaptive control architecture to systems with this integral feedback augmentation while retaining the original control performance of L₁ adaptive control. After some proof and discussions about this method, some simulation examples are given to illustrate the effectiveness of the proposed control methods.