基于Hamilton力学方法的卫星编队高精度相对运动与控制研究

项目名称： 基于Hamilton力学方法的卫星编队高精度相对运动与控制研究

项目编号： No.10802094

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 陈琪锋

作者单位： 中国人民解放军国防科学技术大学

项目金额： 18万元

中文摘要： 本项目系统深入地研究了卫星编队相对运动和最优控制的高精度Hamilton力学建模与求解方法。首先，建立了卫星编队相对运动Hamilton力学模型，分析了相对运动Hamilton函数近似阶数对求解精度的影响。第二，利用相流变换与生成函数的关系，采用生成函数法求解卫星编队相对运动的两点边值问题。第三，在考虑摄动的相对运动Hamilton力学模型基础上研究卫星编队的高精度最优控制问题，提出了基于近似生成函数迭代的求解方法，以计算代价较小的低阶近似逼近高阶精度。第四，针对主体部分可积的Hamilton系统，提出了基于正则摄动理论求解两点边值问题的正则方法，能够考虑Hamilton函数的所有摄动因素，利用该方法高效求解了卫星编队飞行两点边值问题。第五，针对航天动力学问题经常可以分解为一个易于求解的基本问题和相对小的摄动的叠加的特点，提出求解卫星编队Hamilton力学模型与最优控制问题的伪谱迭代法，仅通过线性运算和少量迭代，就能在较大时间域上获得高精度解。第六，利用卫星编队相对运动Hamilton模型第一类生成函数的非负定性，设计了有界摄动力影响下的编队构形重构鲁棒控制器，并进行了仿真验证。

中文关键词： 卫星编队；Hamilton力学；最优控制；生成函数；两点边值问题

英文摘要： The high-precision relative motion and optimal control problem of satellite formation flight based on Hamilton mechanics was systematically investigated in this project. First, the Hamiltonian model of satellite relative motion was built and effect of the order of the approximating Hamiltonian on the precision was analyzed. Second, the relationship of inverse phase flow and the generating functions was explored, and generating function method was used to solve the two point boundary value problems (TPBVPs) of satellite relative motion. Third, on the basis of Hamilton model of satellite relative motion including perturbations, the high precision optimal control problem was studied. An iterative generating function approximation method was proposed to solve the high precision optimal control problem. High order precision was achieved using only low order approximation with small computing cost. Fourth, a canonical method based on canonical perturbation theory was proposed for solving the TPBVPs of Hamilton systems with an integral main part of the Hamiltonian. The method can accommodate all perturbations on the Hamiltonian. It was used to solve the TPBVPs of satellite formation flight. Fifth, based on the observations that many unperturbed astrodynamics problems have already been solved and that perturbations are relatively small, an iterative pseudospectral method was presented to solve the Hamilton models of satellite relative motion and optimal control. Only by linear operations and a few iterations, high precision solutions were obtained on a rather long time domain. Sixth, based on the nonnegativeness of the first class of generating functions of the satellite relative motion, a robust controller under bounded perturbations was designed. Simulations verified the controller design.

英文关键词： satellite formation; Hamilton mechanics; optimal control; generating functions; two point boundary value problems