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, nonsquare multi-input/multioutput 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 allow 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 Luenberger 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/multioutput adaptive controller. A numerical example based on a scramjet-powered blended-wing/body generic hypersonic vehicle model is presented. The six-degree-of-freedom nonlinear vehicle model is linearized, giving the design model for which the controller is synthesized. The adaptive output feedback controller is then applied to an evaluation model, which is nonlinear, coupled, and includes actuator dynamics; and it is shown to result in stable tracking in the presence of uncertainties that destabilize the baseline linear output feedback controller.