Global Tracking Control Structures for Nonlinear Singularly Perturbed Aircraft Systems

Abstract

The problem of simultaneous tracking of both fast and slow states for a general class of nonlinear singularly perturbed systems is addressed. A motivating example is an aircraft tracking a prescribed fast moving target, while simultaneously regulating speed and/or one or more kinematic angles. Previous results in the literature have focused on tracking outputs that are a function of the slow states alone. Moreover, global asymptotic tracking has been demonstrated only for a class of nonlinear systems that possess a unique real root for the fast states. For a more general class of nonlinear systems only local tracking results have been proven. In this paper, control laws that accomplish global tracking of both fast and slow states is developed using geometric singular perturbation methods. Global exponential stability is proven using the composite Lyapunov function approach and an upper bound necessary condition for the scalar perturbation parameter is derived. Controller performance is demonstrated through simulation of a combined longitudinal lateral/directional maneuver for a nonlinear, coupled, six degree-of-freedom model of the F/A-18A Hornet. Results presented in the paper show that the controller accomplishes global asymptotic tracking even though the desired reference trajectory requires the aircraft to switch between linear and nonlinear regimes. Asymptotic tracking while keeping all the closed-loop signals bounded and well behaved is also demonstrated. Additionally the controller is independent of the scalar perturbation parameter nor does it require knowledge of it.