半直接配点法在航天器追逃问题求解中的应用

采用半直接配点法求解时间固定两航天器追逃问题,提出一种新的数值求解追逃双方最优控制策略的方式,避免了求解非线性两点边值问题。在两航天器均为连续小推力假设条件下,以终端距离为支付函数,给出了半直接配点法求解此追逃问题的过程。在此数值方法中,根据半直接转换将微分对策问题转化为一个最优控制问题,由Gauss-Lobbato配点法最终将此最优问题转化为非线性规划问题,继而通过序列二次规划方法求解。这种半直接配点法避免微分对策问题最优策略的必要条件(两点边值问题)求解,并且数值稳定性好。数值仿真给出了追逃双发的最优控制策略和相应的追逃轨迹。     

UKF参数估计在航天器气动辅助变轨问题中的应用

为快速精确地求解气动辅助变轨问题,提出一种基于无损卡尔曼滤波(UKF)参数估计的数值求解方法。首先,针对气动辅助变轨问题,利用极大值原理将其转化为对应的两点边值问题;然后,以协态变量的初值作为估计参数,以末端条件为期望观测值,将该两点边值问题转化为参数估计问题,并应用UKF滤波算法求解。该算法基于估计理论,避免了计算传统数值方法所需要的梯度矩阵,同时克服了猜测协态变量初值的困难,降低了求解气动辅助变轨问题的难度。数值仿真表明,该算法结构简单,求解效率高,具有良好的鲁棒性。     

Method of continuation for optimization of interplanetary low-thrust trajectories

The problem of local optimization of interplanetary low-thrust trajectories is considered with the use of the maximum principle and continuation numerical methods. Two types of problems are analyzed: problems with limited power and problems with limited thrust. The latter problem is generalized by introducing the dependence of thrust and specific impulse on available electric power. In order to reduce the problem of optimal control to a boundary value problem, the Pontryagin maximum principle is used, and then, using the continuation method, this boundary value problem is reduced to the Cauchy problem. Variants of the continuation method for optimizing low-thrust trajectories are presented in the paper, including a new method of continuation for the limited thrust problem, which does not require any choice of the initial approximation for boundary values of conjugate variables.     

Geometric problem solving with strings and pins

Humans solve spatial and abstract problems more easily if these can be visualized and/or physically manipulated. We analyze the domain of geometric problem solving from a cognitive perspective and identify several levels of domain abstraction that interact in the problem solving process. We discuss the roles of physical manifestations of spatial configurations, their manipulation, and their perception for understanding problem solving processes. We propose an extension of the classical problem solving repertoire of constructive geometry to approach certain problems more directly than under the compass-and-straightedge paradigm. Specifically, we introduce strings and pins as helpful metaphors for a generalization of the constructive geometry approach. We present classical problems from spatial problem solving to illustrate the ‘strings and pins’ paradigm. Three case studies are discussed: strings-and-pins solutions to (i) the ellipse construction problem; (ii) the shortest path problem; and (iii) the angle trisection problem. Comparisons to formal solutions are drawn. Differences and similarities between the compass-and-straightedge paradigm and the strings-and-pins paradigm are analyzed. Features and limitations of constructive and depictive geometry as well as implications for computational approaches are discussed. The strings-and-pins domain is shown to be more general and less restrictive than the compass-and-straightedge domain.     

Some new applications of the generalized problem of two fixed centers

A generalized problem of two fixed centers and its limiting version is considered. New possible applications of this problem are obtained. Using a symmetric version of the problem, the external field of gravitation is approximated. The limiting version approximates the inner field.     

地球同步轨道卫星群在轨加注任务规划

以地球同步轨道卫星群为研究对象,开展“多对多”在轨加注任务规划问题研究。首先建立了任务规划的数学模型,该任务规划属于多目标规划问题,求解过程中需要解决TSP问题。其次,给出了该规划问题的求解方法及流程,采用遗传算法进行求解并设计了相应的遗传算子。最后,选取了14颗地球同步轨道卫星作为目标星进行求解,并在小角度近似条件下对计算结果进行了分析,计算结果验证了算法的有效性。     

基于脉冲样本图和Vague集的雷达辐射源识别

针对现有雷达信号特征描述方式很难有效地对复杂雷达辐射源进行描述和识别,提出一种基于脉冲样本图和Vague集的雷达辐射源识别新方法。该方法把雷达辐射源识别问题转换为Vague集的多属性决策问题,不仅能很好地解决雷达信号识别中的模糊问题,而且无需传统方法的特征提取过程,简化了处理环节。另外,基于脉冲样本图的雷达辐射源识别是利用有序的多个脉冲同时匹配识别,因此更可靠。计算机仿真表明该方法是有效可行的,为复杂雷达辐射源识别提供了一种新思路。     

机动目标的空间交会微分对策制导方法

针对目标机动情况,利用定量微分对策方法分析连续推力作用下的空间交会追逃微分对问题,提出用非线性规划求解该微分对策问题的方法,建立空间交会追逃微分对策的非线性规划模型,有效解决了机动目标空间交会微分对策模型高度非线性且难于利用经典最优控制理论进行求解的问题,实现了最优控制与对策论的结合,并通过数值仿真校验了该方法的有效性。     

用DE求解最小能量借力飞行问题

提出了一种差分演化算法（DE）以求解最小能量借力飞行问题。分析借力飞行的物理过程,用演化算法给出最小能量借力飞行的优化模型。优化算例表明：该算法结果较文献更优。     

Symmetric periodic solutions of the Hill’s problem. I

The planar circular Hill’s problem is considered, as well as its limiting integrable variant called the Hénon problem, for which the original Hill’s problem is a singular perturbation. Among solutions to the Hénon problem there are a countable number of generating solutions-arcs that are uniquely determined by the condition of successive passage through the origin of coordinates—singular point of equations of motion of the Hill’s problem. Using the generating solutions-arcs as “letters” of a certain “alphabet”, one can compose, according to some rules, the “words”: generating solutions of families of periodic orbits of the Hill’s problem. The sequence of letters in a word determines the order of orbit transfer from one invariant manifold to another, while the set of all properly specified words determine the system’s symbolic dynamics.