ℒ₁ adaptive augmentation of gain-scheduled controller for racetrack maneuver in aerial refueling

In this paper we present the ℒ₁ adaptive controller for time-varying reference systems. This extension is motivated by the need for augmentation of baseline gain-scheduled controller, which naturally leads to a time-varying reference system. Keeping this in mind, the synthesis of ℒ₁ adaptive controller in this paper pursues two objectives. First, the adaptive augmentation must recover the nominal performance of the gainscheduled controlled system at different operating points, without overruling the performance of the baseline controller. Second, the design of the adaptive augmentation should be pursued in a way so that in the absence of uncertainties the output of it is zero. Thus, the adaptive augmentation must include the dynamics of the closedloop system, controlled by the baseline gain-scheduled controller, as a part of its feedback. The dynamics of the gain-scheduled controller change dependent upon the scheduling variables, resulting in a time-varying closed-loop reference system with a "slow rate" of variation. In this paper, we analyze the stability and the performance of the ℒ₁ adaptive controller for a time-varying reference system. We show that the ℒ₁ adaptive augmentation of the baseline gain-scheduled controller does not require a "slower rate" of variation for the scheduling variables, used in the design of baseline gain-scheduled controller. The performance of the gainscheduled controller can be retained by uniformly increasing the rate of adaptation. We further illustrate how the theory can be used for adaptive augmentation of a baseline gain-scheduled controller by simulating racetrack maneuver of autonomous aerial refueling.