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Indexed by:期刊论文

Date of Publication:2015-11-02

Journal:INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

Included Journals:SCIE、EI

Volume:92

Issue:11

Page Number:2273-2289

ISSN No.:0020-7160

Key Words:optimal control problem; Hamiltonian system; boundary-value problem; hypersensitive problem; symplectic algorithm

Abstract:A symplectic algorithm with nonuniform grids is proposed for solving the hypersensitive optimal control problem using the density function. The proposed method satisfies the first-order necessary conditions for the optimal control problem that can preserve the structure of the original Hamiltonian systems. Furthermore, the explicit Jacobi matrix with sparse symmetric character is derived to speed up the convergence rate of the resulting nonlinear equations. Numerical simulations highlight the features of the proposed method and show that the symplectic algorithm with nonuniform grids is more computationally efficient and accuracy compared with uniform grid implementations. Besides, the symplectic algorithm has obvious advantages on optimality and convergence accuracy compared with the direct collocation methods using the same density function for mesh refinement.