caa a22 4500 445863501 CHVBK 20180317145450.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s10569-011-9360-4 doi (NATIONALLICENCE)springer-10.1007/s10569-011-9360-4 Symplectic adaptive algorithm for solving nonlinear two-point boundary value problems in Astrodynamics [Elektronische Daten] [H. Peng, Q. Gao, Z. Wu, W. Zhong] In this paper, from a Hamiltonian point of view, the nonlinear optimal control problems are transformed into nonlinear two-point boundary value problems, and a symplectic adaptive algorithm based on the dual variational principle is proposed for solving the nonlinear two-point boundary value problem. The state and the costate variables within a time interval are approximated by using the Lagrange polynomial and the costate variables at two ends of the time interval are taken as independent variables. Then, based on the dual variational principle, the nonlinear two-point boundary value problems are replaced by a system of nonlinear equations which can preserve the symplectic structure of the nonlinear optimal control problem. Furthermore, the computational efficiency of the proposed symplectic algorithm is improved by using the adaptive multi-level iteration idea. The performance of the proposed algorithm is tested by the problems of Astrodynamics, such as the optimal orbital rendezvous problem and the optimal orbit transfer between halo orbits. Springer Science+Business Media B.V., 2011 Nonlinear optimal control nationallicence Two-point boundary value problem nationallicence Dual variational principle nationallicence Adaptive symplectic algorithm nationallicence Astrodynamics nationallicence Halo orbits nationallicence Peng H. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, 116024, Dalian, China aut Gao Q. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, 116024, Dalian, China aut Wu Z. School of Aeronautics and Astronautics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, 116024, Dalian, China aut Zhong W. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, 116024, Dalian, China aut Celestial Mechanics and Dynamical Astronomy Springer Netherlands 110/4(2011-08-01), 319-342 0923-2958 110:4<319 2011 110 10569 https://doi.org/10.1007/s10569-011-9360-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-011-9360-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Peng H. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, 116024, Dalian, China aut NATIONALLICENCE 700 1- Gao Q. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, 116024, Dalian, China aut NATIONALLICENCE 700 1- Wu Z. School of Aeronautics and Astronautics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, 116024, Dalian, China aut NATIONALLICENCE 700 1- Zhong W. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, 116024, Dalian, China aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 110/4(2011-08-01), 319-342 0923-2958 110:4<319 2011 110 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer