A robust adaptive control architecture with L∞ transient and steady-state performance guarantees

In this paper, a new adaptive control architecture for nonlinear uncertain dynamical systems is developed to address the problem of high-gain adaptive control. Specifically, the proposed framework involves a new and novel controller architecture involving a modification term in the update law that minimizes an error criterion involving the distance between the weighted regressor vector and the weighted system error states. This modification term allows for fast adaptation without hindering system robustness. In particular, we show that the governing tracking closed-loop system error equation approximates a Hurwitz linear time-invariant dynamical system with L_∞ input-output signals. This key feature of our framework allows for robust stability analysis of the proposed adaptive control law using L₁ system theory. We further show that by properly choosing the design parameters in the modification term we can guarantee a desired bandwidth of the adaptive controller, guaranteed transient closed-loop performance, and an a priori characterization of the size of the ultimate bound of the closed-loop system trajectories.