Shortcut-time spatial trajectories on-board optimization and their cognitive head-up display visualization for pilot's control actions during manoeuvring support

Considers the general aspects of mathematical foundation of on-board universal pilot's support system subsystem, which provides pilot's control actions support during more or less long-term maneuvers, such as take-off and climbing, flight on a route, surface-based target attack (in case of military aircraft), descent and landing via shortcut-time spatial trajectories on-board optimization and their head-up display in the view of "road-in-the-sky" image visualization for its further tracking in direct with foresee regime or (semi) automatic mode. Two specially designed modifications of direct method of variational tasks solution are disclosed-one (for short-term trajectories with strong restrictions on control functions) based on 5th-7th power polynomials optimal trajectory approximation, the second (for long-term flight on a route trajectories) based on spline approximation. Both from a conditional arch argument, with obligatory satisfaction of phase coordinates and control boundary conditions (a priori) and all limitations (in the process of optimization). The paper includes examples of computer-based high maneuverable airplane tactical simulator with demonstrated prototype of considered subsystem.