基于二代小波的轨迹优化节点自适应加密

丰志伟; 张青斌; 唐乾刚; 张永合

基于二代小波的轨迹优化节点自适应加密

1.
国防科学技术大学航天科学与工程学院, 长沙 410073
2.
中国科学院上海微系统与信息技术研究所, 上海 200050

基金项目: 国家自然科学基金(11272345)

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出版历程
- 收稿日期: 2012-11-09
- 刊出日期: 2013-07-28

Node adaptive refinement for trajectory optimization based on second-generation wavelets

1.
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
2.
Shanghai Institute of Microsystem and Information, Chinese Academy of Science, Shanghai 200050, China

摘要

摘要: 针对采用直接法求解轨迹优化问题中精度和效率之间的矛盾,提出了基于二代小波轨迹优化节点自适应加密.采用RK(Runge-Kutta)离散方法将原轨迹优化问题转化为非线性规划问题,并采用成熟的非线性规划算法求解.对控制或状态函数进行小波变换得到小波系数,基于小波系数和二分节点的对应关系,根据小波系数的幅值确定下一个迭代步所使用的节点并进行序列优化.算例结果表明:通过设置合适的小波系数阀值,采用较少的时间离散节点即可使优化结果达到预定的精度.与高斯伪谱法软件相比,节点个数大约减少10%,最优指标的精度大约提高1个数量级.
- 轨迹优化 /
- 节点自适应 /
- 直接法 /
- 二代小波 /
- 多分辨分析
Abstract: A mesh adaptive refinement method for solving trajectory optimization problem by using direct method based on second-generation wavelets was proposed to deal with the conflict between accuracy and efficiency. The original trajectory optimization problem was transformed into a nonlinear programming problem that was solved by standard nonlinear programming codes. Then the wavelet transformation of control or state function was performed, and the wavelet coefficients were obtained. A new node could be determined based on the magnitude of coefficients and the relationship between wavelet coefficients and dyadic nodes. The results demonstrate that the proposed method can balance accuracy of the solution and speed of computations by setting appropriate threshold of wavelet coefficients. Compared with the Gauss pseudospectral method software package, the number of nodes are reduced by 10% approximately, and the optimality accuracy is increased by an order of magnitude by using the method.
- trajectory optimization /
- node adaptive /
- direct method /
- second generation wavelets /
- multi-resolution analysis

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参考文献(15)

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