Transfer of a Dynamic Object onto the Surface of an Ellipsoid
- Authors: Akulenko L.D.1, Shmatkov A.M.1
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Affiliations:
- Institute for Problems in Mechanics
- Issue: Vol 57, No 1 (2018)
- Pages: 63-71
- Section: Optimal Control
- URL: https://journals.rcsi.science/1064-2307/article/view/220068
- DOI: https://doi.org/10.1134/S1064230718010021
- ID: 220068
Cite item
Abstract
Using Pontryagin’s maximum principle, the problem of the quickest transfer of a multidimensional object onto the surface of an ellipsoid is reduced to solving a scalar algebraic equation. The concentration of the endpoints of optimal trajectories in the vicinity of the points forming the boundary in the case of a degenerate ellipsoid is demonstrated. An example in which the optimal control has a jump and the Bellman function has a discontinuity when the magnitude of the initial velocity vector undergoes a small change is constructed. It is also shown that the jump in the optimal control can occur without the discontinuity of the Bellman function.
About the authors
L. D. Akulenko
Institute for Problems in Mechanics
Email: shmatkov@ipmnet.ru
Russian Federation, Moscow, 119526
A. M. Shmatkov
Institute for Problems in Mechanics
Author for correspondence.
Email: shmatkov@ipmnet.ru
Russian Federation, Moscow, 119526