Novel Approaches in Optimal Control and Their Application to Find Analytical Solutions for Minimum-Time Ascending Maneuver

Abstract

Of utmost importance to development of UAVs, is an automatic flight system. Minimum-time maneuvers however, are most challenging due to the fact that dynamic and kinematic constraints should not be violated while conservative assumptions on actuator limits, compromise optimality. A major hindrance in minimum time to climb is that the kinematic constraint introduces a redundant state which makes the Hamiltonian quite difficult to handle while numerical methods are distrustful for that the resulting system of two-point boundary value problem is unbounded. To overcome these, a novel approach to a class of problems will be suggested. It is proved herein how this method allows the cost functional to be changed so that the number of state variables is reduced. These results facilitate the finding of the analytical optimal solution to reaching a waypoint with any initial but no final boundary conditions on the angle of trajectory. For when the final angle of the trajectory is specified, a method will be proposed. The solutions found here can be used by an RHPC method.