Adaptive control with magnitude and rate limited observer-based disturbance rejection

This paper considers the problem of controlling a piecewise continuously differentiable system subject to time-varying matched uncertainties. The uncertainties are decomposed into two parts: a time-invariant linearly-parameterized portion and a time-varying unstructured portion. The former is addressed using conventional model reference adaptive control, while the latter is handled by disturbance observer-based control. The objective is to ensure good performance through observer-based disturbance rejection when possible, while preserving the robustness guarantees of adaptive control. A key feature of the observer-based disturbance compensation is a magnitude and rate limited integral action that prevents fast fluctuations in the control command due to the observer dynamics.