点击次数：

论文类型：期刊论文

发表时间：2017-01-01

发表刊物：COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

收录刊物：SCIE、EI

卷号：42

页面范围：623-644

ISSN号：1007-5704

关键字：Nonlinear optimal control; Symplectic; Pseudospectral method; Variational principles; hp method; Hamiltonian system

摘要：An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method. (C) 2016 Elsevier B.V. All rights reserved.