Differential Flatness of Aircraft Flight Dynamics and Neural Inversion

Differential flatness, a property of some dynamic systems, introduced by Fliess et al., has made possible the development of new tools to control complex nonlinear dynamic systems. Many dynamic non linear systems have been proved to be differentially flat. Some authors have investigated the differential flatness of conventional aircraft dynamics, although none of them has considered separately the flatness property of the flight guidance and the attitude dynamics of a rigid aircraft. In this paper, it is shown that the inertial position coordinates of an aircraft can be considered as differential flat outputs for its flight guidance dynamics. Since this differential flatness property is implicit, a neural network is introduced, as a numerical device, to deal with the inversion of the guidance dynamics. It is shown also that, once conveniently structured and trained, the neural network is able to generate in real time directives to conventional autopilot systems concerned with attitude and engine regime control so that the reference trajectory can be tracked. Numerical simulation results are displayed and discussed.