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. The problem of analytical synthesis of the control acceleration for an unmanned aerial vehicle (UAV) during its flight along a complex trajectory, consisting of sequentially located horizontal flight sections, located at different heights relative to the earth's surface has been solved in the paper. The problem has been solved as an analytical definition of the optimal control of a linear non-stationary system for a specified minimized quality functional. The mathematical model of the system is presented in the form of differential equations of UAV motion in the vertical plane of a fixed coordinate system related to the earth's surface. A feature of the proposed methodology for solving the problem is the substantiation of the original form of the minimized functional and parameters included in the law of variation of the control acceleration obtained by known methods. As the components of the quality functional, the values of coordinates and velocity of the UAV are considered and they are specified at the corresponding points in space through which the UAV path must pass, in order to obtain the optimal curvature of the trajectory. The derived mathematical dependences make it possible to implement them on board of an aircraft and, ultimately, solve the problem of ensuring the minimum energy consumption when controlling an object (UAV). Computer simulation of the analytically obtained results in the form of the UAV flight trajectory and the processes of changing its acceleration and speed have shown the efficiency of the proposed technique and the prospects of its use at the initial stage of the synthesis of the UAV control system.

The problem of the stage-by-stage synthesis of the mathematical model of the autopilot of an unmanned aerial vehicle (UAV) is considered. At the first stage, an analytical synthesis of the control acceleration applied to the center of mass of the UAV is performed to form a specified trajectory of its flight. On the basis of the results received at the first stage, at the subsequent stages, the problem of synthesizing a mathematical model of the UAV autopilot is solved with the specified requirements for ensuring the stability and dynamic accuracy of UAV control. Under actual assumptions about the corresponding nature of changes in the trajectory parameters and variables that characterize the motion of the UAV in space, the use of a linear mathematical model of the evolution of the state vector of the UAV and its control system is substantiated. When synthesizing a mathematical model of the UAV autopilot, the method of modal control of the system was used for a specified mathematical model of the object. For a specified model of motion and aerodynamic characteristics of the UAV, the law of deviation of the control steering surface is analytically received, which depends on the parameters of the translational and rotational movement of the UAV. Computer simulation of the analytically received results of control synthesis for the specified characteristics of UAVs and specific using conditions was carried out, which clearly showed the efficiency and prospects of using this approach for the synthesis of control systems for UAVs of various purposes and design.

The problem of determining the shape and parameters of a mathematical model in the form of a transfer function for the movement of an unmanned aerial vehicle (UAV) in the vertical plane of space is solved. The angle of deviation of the Elevator is considered as the input signal, and the pitch angle of the UAV is considered as the output signal. We use the results of experimental studies of UAV flight, which are considered as known values of input and output signals under specified flight conditions. The measured discrete values of the experimental results are approximated by a fourth-order polynomial based on regression analysis for ease of use in identification. The analytical substantiation of the need to apply the methods of linearization of the mathematical model of UAV movement and the accepted assumptions for obtaining differential equations of UAV movement relative to the center of mass, allowing to synthesize the required transfer function of the corresponding element of the UAV control system. The results of computer modeling confirmed the validity of the synthesized mathematical model obtained on the basis of structural and parametric identification. This approach can be used to obtain simplified mathematical models that are used to solve problems of synthesis and optimization of control systems not only for UAVS, but also for other dynamic objects.