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论文类型：期刊论文

发表时间：2015-11-02

发表刊物：INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

收录刊物：SCIE、EI

卷号：92

期号：11

页面范围：2273-2289

ISSN号：0020-7160

关键字：optimal control problem; Hamiltonian system; boundary-value problem; hypersensitive problem; symplectic algorithm

摘要：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.