Output-Feedback I&I Adaptive Control for Linear Systems with Time-Varying Parameters

This paper combines the so-called congelation of variables method with the adaptive immersion and invariance (I&I) approach to control linear single-input-single-output systems with time-varying parameters via output feedback. The system is first reparameterized using a pair of reduced-order filters and the reparameterization error dynamics show that the input is coupled with a time-varying perturbation. By exploiting the input-to-state stability (ISS) of the inverse dynamics, which is regarded as a counterpart in the time-varying setting of the classical minimum-phase property, the coupling between the input and the time-varying perturbation is transformed into a coupling between the output and another time-varying perturbation that can be dominated in the controller design stage. A pair of high-gain filters are then implemented so that the reparameterization error dynamics are ISS. Finally, output regulation is achieved by strengthened damping design, which invokes a small-gain-like argument from a Lyapunov perspective.