Symplectic algorithms with mesh refinement for a hypersensitive optimal control problem

作     者：Peng, Haijun Gao, Qiang Wu, Zhigang Zhong, Wanxie 

作者机构：Dalian Univ Technol Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Sch Aeronaut & Astronaut Dalian 116024 Peoples R China 

出 版 物：《INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS》 (国际计算机数学杂志)

年 卷 期：2015年第92卷第11期

页      面：2273-2289页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation of China [11102031, 11472069, 11272076] China Postdoctoral Science Foundation [2014M550155] Fundamental Research Funds for Central Universities [DUT13LK25] Liaoning Province Education Administration [L2013015] State Key Laboratory of Mechanics and Control of Mechanical Structures [MCMS-0114G02] 

主　　题：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.