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论文类型：期刊论文

发表时间：2011-08-01

发表刊物：CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY

收录刊物：SCIE

卷号：110

期号：4

页面范围：319-342

ISSN号：0923-2958

关键字：Nonlinear optimal control; Two-point boundary value problem; Dual variational principle; Adaptive symplectic algorithm; Astrodynamics; Halo orbits

摘要：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.