An Adaptive Law with Tracking Error Dependent Adaptive Gain Adjustment Mechanism

Abstract

In many practical implementations of adaptive control laws it is of interest to limit the aggressiveness of the adaptive control law until it is needed in cases of abnormal operation. Many approaches have been taken in an ad hoc manner such as gain scheduling the adaptive gains or using switching mechanisms. However, none of these techniques offer a theoretically justified means of adjusting the adaptive control law in response to abnormal conditions. This paper presents a state feedback method for smoothly adjusting the adaptive gain of an adaptive law in response to increased levels of tracking error. This method allows a control designer to specify how the adaptive law adjusts its gain in response to increased tracking error. The effect of the gain adjustment process is reflected in an analysis of system tracking bounds. As the system tracking error increases, the gain adjustment mechanism warps the Lyapunov level sets in a manner that ensures tracking error remains small. The tracking bound analysis allows the theoretically guaranteed tracking bounds to be made small without necessarily requiring high adaptation gain. This offers a significant improvement over existing theoretical performance bounds.