Section: Application Domains
In  and  , we applied the technique of backstepping and of construction of strict Lyapunov functions to solve a tracking probelm for the celebrated aircraft model PVTOL (Planar Vertical Takeoff and Landing). It is a benchmark dynamics for an aircraft moving in a vertical plane that contains the important features needed to design controllers for real aircraft. The controllers are the thrust out of the bottom and the rolling moment controller. The main challenges are that the thrust controller must remain nonnegative and that the system is underactuated. We overcame these challenges through a change of variables that transforms the PVTOL tracking dynamics into a chain of three subsystems and then applying asymptotic strict Lyapunov function methods and bounded backstepping. Relative to the PVTOL model literature, the significance of our PVTOL work was (a) the global boundedness of our controllers in the decoupled coordinates, (b) their applicability to cases where the velocity measurements are not available, by using an observer, (c) the positive lower bound on the thrust controller, (d) our allowing a very general class of reference trajectories, and (e) our use of ISS to certify good performance under actuator errors, which would not be possible using LaSalle invariance or nonstrict Lyapunov functions.