The Output of a Group of Aircraft to a Given Position at a Given Time

The article considers an algorithm for controlling a group of aircraft providing a given location of aircraft in space at a given time. When controlling a group of unmanned aerial vehicles, it is often necessary to bring them to the specified positions at a given time. Reachability areas and optimal control methods can be used to bring aircraft to specified positions. The application of reachability domains for solving problems of controlling a group of aircraft is considered. The article also provides an analysis of the method of calculating the reachability areas and an example of calculating the reachability areas of a rocket. A problem for a group of aircraft is considered, for which reachability domains are used in a group way. Aircraft with specific characteristics and initial parameters are used for modeling. The task is solved in two stages. The reachability regions in the vertical plane are approximated by triangles. The equations were integrated by the Runge-Kutta method with a constant step. For an aircraft whose motion is determined by a system of equations with a control constraint under given initial conditions, it is necessary to define a control program that provides a minimum of functionality. Thus, the optimal control problem is reduced to a boundary value problem: to find a solution to a system of equations whose phase coordinates satisfy the initial conditions and boundary conditions. In addition, according to the maximum principle, the Hamilton function under optimal control should reach a maximum. Moreover, the control must satisfy the restriction. The construction of reachability areas and the choice of programs based on the maximum principle makes it possible to bring a group of aircraft to a given position at a given time.