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• W3208264299 abstract "Second-order optimality conditions for fuel-optimal control problems with both endpoints on manifolds are studied in this paper. Each candidate extremal from Pontryagin’s maximum principle is embedded into a parameterized family of extremals, and two no-fold conditions for the projection of the parameterized family onto state space to be a diffeomorphism are devised. By the theory of field of extremals, the no-fold conditions are related to the classical second-order conditions for the absence of conjugate points or focal points. Thus, the no-fold conditions are sufficient to ensure the candidate extremal to be locally optimal if the initial state is fixed. When the initial state is not fixed but lies on a manifold, an additional second-order optimality condition involving the geometry of the initial constraint manifold is established. A numerical procedure for testing all the second-order conditions is presented, allowing to check the optimum of each candidate extremal. Finally, three fuel-optimal orbital transfer problems in the Earth–moon–spacecraft system are computed, demonstrating and verifying the developments of the paper." @default.
• W3208264299 created "2021-11-08" @default.
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• W3208264299 date "2022-02-01" @default.
• W3208264299 modified "2023-10-16" @default.
• W3208264299 title "Second-Order Conditions for Fuel-Optimal Control Problems with Variable Endpoints" @default.
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• W3208264299 doi "https://doi.org/10.2514/1.g005865" @default.
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