The problem of trajectory tracking control for an underactuated stratospheric airship with model parameter uncertainties and wind disturbances is addressed in the paper. An adaptive backstepping sliding-mode controller is designed from the airship nonlinear dynamics model. The proposed controller has a two-level structure for trajectory guidance, tracking and stability, and the developed controller, based on nonlinear adaptive sliding-mode backstepping method, provides airship attitude and velocity control for the entire flight process. Furthermore, an active set based weighted least square algorithm is applied to find the optimal control surface inputs and the thruster commands under constraints of actuator saturation. The closed-loop system of trajectory tracking control plant is proved to be globally asymptotically stable by using Lyapunov theory. By comparing with traditional backstepping control and PID design, the results obtained demonstrate the capacity of the airship to execute a realistic trajectory tracking mission under two cases of lateral- and roll- underactuations, even in the presence of aerodynamic coefficient uncertainties, and wind disturbances
