Formation of the Trajectory of Controlled Aircraft

Currently, there is an increased interest in the creation of flight control systems for unmanned aerial vehicles, which, taking into account real conditions, would ensure its trajectory and thereby determine the effectiveness of the use of the aerial vehicle. Aircraft navigation, in particular ballistic cruise missiles, requires the formation of high-precision control in order to achieve both final results and local optimization tasks at each of the flight stages: take-off, departure to set trajectories, maneuvering, etc. The development of admissible control and its optimization by computer-mathematical methods of modeling and optimization is a time-consuming process and requires significant expenditures of various types of resources. An element of the effectiveness of such a mathematical apparatus for guaranteeing and increasing the reliability and effectiveness in achieving the set goal is the speed of calculations, which, in turn, requires the simplification of the mathematical model by obtaining functional dependencies for calculating the flight trajectory, avoiding complex mathematical calculations. The complete working model for calculating the desired trajectory of the aircraft will be determined by the specified control functions and will be provided by a system of partial differential equations with time, and the necessary parameters for calculating all aerodynamic forces and moments are tabular data in most cases. A mathematical model for solving the task of forecasting navigation for such complex controlled systems is proposed to be carried out using two coordinate systems: starting and speed. Moreover, all calculations of the velocity vector, which depends on the net effect of three aerodynamic forces acting on the aircraft, should be carried out in the speed coordinate system, and coordinate control of the flight along the entire dynamic trajectory should be determined in the starting system