Speaker
Mr
Ilia Nikolichev
(Moscow Aviation Institute)
Description
The possibility of using the method of dual numbers in automatic differentiation for solving optimization problems of the low-thrust multi-revolution orbital transfers is considered. Traditionally the motion equations for the spacecraft with electric propulsion for multi-revolution orbital transfers are written in osculating elements or their modifications which exclude the special features in the right-hand sides of differential equations. These right-hand sides of the equations become especially complicated when different perturbations influencing the spacecraft movement are taken into account. Within the formalism of the Pontryagin maximum principle the right-hand sides of the optimal motion equations for the adjoints equations are quite complicated which results in some difficulties in solving optimization problems. Therefore the use of dual numbers method in numerical differentiation of optimal Hamiltonian for calculating the right-hand sides of the optimal motion equations of the spacecraft is effective. Another aspect of using the dual numbers method for numerical differentiation is to calculate the sensitivity matrix when solving boundary value problem corresponding to the optimal control problem. In this case, using dual numbers method allows obtaining the accurate sensitivity matrix. When using the continuation method for solving boundary value problem it helps to improve the convergence and to significantly reduce the number of steps for the external integration of Cauchy problem. The numerical results for optimal multi-revolution orbital transfer from the arbitrary initial orbit into the geostationary orbit are presented.
| Applicant type | First author |
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Primary author
Mr
Ilia Nikolichev
(Moscow Aviation Institute)
Co-author
Prof.
Mihkail Konstantinov
(MAI)
