UAV path following using a mixed piecewise-affine and backstepping control approach

This paper combines for the first time piecewise-affine (PWA) and backstepping control approaches applied to path following for a simplified longitudinal model of an Uninhabited Aerial Vehicle (UAV). For controller design purposes, the overall dynamics of the UAV are divided into two sets of dynamics that are in cascade connection. One set of dynamics describes the steering motion of the UAV and another set describes the translational motion of the UAV, where both motions are in the longitudinal plane. Each set is treated separately in the controller design, and stability of the overall system is guaranteed. While assuming the translational velocity constant, a PWA state feedback controller is designed for the dynamics of the steering subsystem of the UAV. The search for the parameters corresponding to the PWA controller and to a globally quadratic Lyapunov function is formulated as an optimization problem subject to linear and bilinear matrix inequality constraints. Then, a backstepping type approach is used to step back from the translational velocity to the input force, where a nonlinear controller is designed for the dynamics of the translational velocity subsystem of the UAV. The proposed method is demonstrated through a numerical example of a UAV performing a loop in the longitudinal plane.