On Achieving Predictable Adaptive Control Response for Uncertain Dynamical Systems with Large Domains of Operation

While adaptive control has been used in numerous applications, the ability to obtain a predictable transient and steady-state system response is still an open problem for dynamical systems with large system uncertainties and without a priori knowledge of a conservative upper bound on their unknown ideal weights. In order to address this problem, recently a novel command governor architecture was constructed for adaptive stabilization and command following. It was shown that by choosing the design parameter of the command governor, the controlled nonlinear uncertain dynamical system can approach a Hurwitz linear time-invariant dynamical system with L∞ input-output signals without resorting to high-gain learning rates in the adaptation law. Even though the proposed architecture was shown to be effective and can operate in larger domains with predictable transient and steady-state system response as compared with the standard adaptive controllers, it may result in control signals having high-frequency oscillations as the magnitude of the tracking commands gets larger. This is due to the fact that the controlled uncertain dynamical system subject to a large tracking command behaves as a controlled uncertain dynamical system having high-gain learning rates, although the learning rate of the command governor-based adaptive controller is chosen to be low-gain. To that end, this paper proposes a novel modification to the weight update law that couples the command governor with the adaptive controller. Specifically, this modification filters out the high-frequency content contained in the weight update law while preserving the asymptotic stability of the system error dynamics, and hence, it enables the proposed command governor-based adaptive controller to maintain its performance in the face of applied tracking commands operating the uncertain dynamical system in large domains and/or subject to high-gain learning rates.