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论文类型：期刊论文

发表时间：2015-12-01

发表刊物：INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS

收录刊物：SCIE、EI、Scopus

卷号：12

期号：6

ISSN号：0219-8762

关键字：Optimal control problems; symplectic numerical method; pseudospectral method; irregular interpolation; variational principle

摘要：Symplectic numerical methods for optimal control problems with irregular interpolation schemes are developed and the comparisons between irregular interpolation schemes and equidistant scheme are made in this paper. The irregular interpolation points, which are the collocation points usually adopted by pseudospectral (PS) methods, such as Legendre-Gauss, Legendre-Gauss-Radau, Legendre-Gauss-Lobatto and Chebyshev-Gauss-Lobatto points, are taken into consideration in this study. The symplectic numerical method with irregular points is proposed firstly. Then, several examples with different complexities highlight the differences in performance between different kinds of interpolation schemes. The numerical results show that the convergence of the present symplectic numerical methods can be obtained by increasing the number of sub-intervals or the number of interpolation points. Moreover, the comparison results show that the convergence of the symplectic numerical methods are generally independent on the type of interpolation points and the computational efficiency is not sensitive to the choice of interpolation points in general. Thus, the symplectic numerical methods with different interpolation schemes have obvious difference with the PS methods.