Algorithm for optimizing the trajectory of an aircraft climbing under uncertainty

The article solves the problem of synthesizing optimal trajectory control for a maneuverable aircraft, which is relevant at the stage of preliminary aerodynamic design when calculating the flight radius under uncertainty arising from a lack of statistical information and knowledge. As part of solving this problem, an algorithm for optimizing the trajectory in the phase space is proposed based on the integration of the direct collocation method that provides high computational efficiency and stability of the solution for nonlinear dynamic models, and uncertainty theory that allows taking into account the non-determinism of input parameters caused by the need to use expert information in the formation of initial data. The direct collocation approach is superior to traditional algorithms based on solving the Riccati equations and the single shooting method. The uncertainty theory provides an effective framework for calculations involving non-deterministic parameters that are set by experts. The advantages of the developed algorithm include versatility, high accuracy, and applicability to complex nonlinear systems when using inaccurate data. The paper presents a mathematical formulation of the problem in which a non-deterministic objective function is replaced by its numerical characteristic, a description of the developed algorithm and the results of computational studies demonstrating the possibility of combining the direct collocation method and uncertainty theory to form reliable solutions for trajectory control.