Low-frequency learning and fast adaptation in model reference adaptive control for safety-critical systems

While adaptive control has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the necessity of high-gain learning rates to achieve fast adaptation can be a serious limitation of adaptive controllers. This is due to the fact that fast adaptation using high-gain learning rates can cause high-frequency oscillations in the control response resulting in system instability. In this paper, we present a new adaptive control architecture for nonlinear safety-critical uncertain dynamical systems to address the problem of achieving fast adaptation using high-gain learning rates. The proposed framework involves a new and novel controller architecture involving a modification term in the update law. Specifically, this modification term filters out the high-frequency content contained in the update law while preserving asymptotic stability of the system error dynamics. This key feature of our framework allows for robust, fast adaptation in the face of high-gain learning rates. Furthermore, we show that transient and steady-state system performance is guaranteed with the proposed architecture. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.