Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

Abstract

This paper presents a new method of synthesizing an output feedback adaptive controller for a class of uncertain, non-square, multi-input multi-output systems that often occur in hypersonic vehicle models. The main challenge that needs to be addressed is the determination of a corresponding square and strictly positive real transfer function. This paper proposes a new procedure to synthesize two gain matrices that allows the realization of such a transfer function, thereby allowing a globally stable adaptive output feedback law to be generated. The unique features of this output feedback adaptive controller are a baseline controller that uses a Luen- berger observer, a closed-loop reference model, manipulations of a bilinear matrix inequality, and the Kalman- Yakubovich Lemma. Using these features, a simple design procedure is proposed for the adaptive controller, and the corresponding stability property is established. The proposed adaptive controller is compared to the classical multi-input multi-output adaptive controller. A numerical example based on a 6 degree-of-freedom nonlinear, scramjet powered, blended wing-body generic hypersonic vehicle model is presented. The adaptive output feedback controller is applied to result in stable tracking of uncertainties that destabilize the baseline linear output feedback controller.