Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
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On the structure of the optimal thrust for the “intermediate” aircraft model

Published: 10.06.2020

Authors: Cherkasov O. Yu., Smirnova N.V.

Published in issue: #6(102)/2020

DOI: 10.18698/2308-6033-2020-6-1991

Category: Aviation and Rocket-Space Engineering | Chapter: Aircraft Dynamics, Ballistics, Motion Control

The paper considers a brachistochrone problem modification including in the objective function a fuel consumption penalty apart from the process time. The material point moves in a vertical plane under gravity, viscous nonlinear friction and traction. The trajectory slope angle and thrust are considered as a control variables. The Pontryagin maximum principle allows reducing the optimal control problem to a boundary value problem for a system of two nonlinear differential equations. Qualitative analysis of the resulting system allows studying the key features of extreme trajectories, including their asymptotic behavior. Extreme thrust control is obtained as a function of the velocity and the trajectory slope angle. The structure of extreme thrust is determined, and the number of switches is analytically determined. The results of numerical solving the boundary value problem are presented, illustrating the analytical conclusions.

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