Airplane trajectory expansion for dynamics inversion

In aircraft research, there is keen interest in the procedure of determining the set of controls required to perform a maneuver from a definition of the trajectory. This is called the inverse problem. It has been proposed that if a complete set of states and state time derivatives can be derived from a trajectory then a model-following solution can allocate the controls necessary for the maneuver. This paper explores the problem of finding the complete state definition and provides a solution that requires numerical differentiation, fixed point iteration and a Newton's method solution to nonlinear equations. It considers trajectories that are smooth, piecewise smooth, and noise ridden. The resulting formulation was coded into a FORTRAN program. When tested against simple smooth maneuvers, the program output was very successful but demonstrated the limitations imposed by the assumptions and approximations in the development.