Trajectory Simulation of a High-Speed Gliding Vehicle Considering Uncontrolled Disturbances Using the Simplex Method

High-speed vehicles are characterized by velocities significantly exceeding the speed of sound and possess dynamic properties that complicate their monitoring by various radio-electronic means. This article develops an approach to generate a set of trajectories for the center of mass of a high-speed gliding vehicle, accounting for the influence of a wide range of random, uncontrolled factors, such as wind gusts, turbulence, and atmospheric density variations. The objective is to form a reachable set in the state vector space of the vehicle. A mathematical model for the spatial motion of the high-speed vehicle’s center of mass is proposed, considering the aforementioned disturbing factors. The motion is assumed to follow a guidance law, considered as an analogue of the proportional navigation method. A specific feature of the problem under consideration is that the generated trajectories must, with the given confidence probability, envelope certain closed regions of space, defined by a priori known coordinates and dimensions. The authors interpret this problem as a dual one: first, as a problem of generating a nominal trajectory for the high-speed vehicle in the absence of disturbances, formulated as a nonlinear programming problem and solved using the Nelder–Mead simplex method; and second, as a problem of piecewise program control for the vehicle’s center of mass motion under disturbances, employing a proportional–integral–derivative controller for altitude channel stabilization.