航天器在远制导阶段非中心地球重力场下收敛的能量最优控制

Q3 Mathematics SPIIRAS Proceedings Pub Date : 2019-02-21 DOI:10.15622/SP.18.1.202-229
V. Mironov, Y. Mironov, I. Fominov
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引用次数: 0

摘要

本文研究了利用庞特里亚金最大原理计算远程制导阶段控制航天器接近轨道目标的能量最优程序的算法发展。假设航天器配备了以化学燃料为动力的纵向推进系统。确定二次油耗最优变化方案和余弦导矢量,确定推进系统推力方向。作为最优控制的标准,我们考虑一个函数,它决定了工作流体的最小消耗。最优控制问题是在状态空间的一个有限区域内解决的,该区域由航天器在一圈内的角距变化范围决定。利用物体在地球法向引力场中的运动模型,给出了极大值原理边值问题的完整方程、边界条件以及决定最优模式下控制结构的解析依赖关系。用牛顿法求解边界优化问题。为了确定共轭变量的初始逼近,给出了均匀中心场下能量最优逼近控制问题的解析解。给出了远程制导阶段控制地球法向引力场末距拦截的能量优化方案的数值研究结果。一般来说,在机载和地面复杂环境中使用最优进近控制算法,可以在执行机动时减少燃料成本,减少时间,并扩大目标物体的可达区域。此外,最优解可以作为参考,有必要比较各种近似控制算法的变体,评估其质量,并对其实际使用做出明智的决策。
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Energetically Optimal Control of the Convergence of the Spacecraft in Non-Central Gravitational Field of the Earth on the far Guidance Stage
The article is devoted to the development of algorithms for calculating energy-optimal programs for controlling the approach of a spacecraft to an orbital object at the long-range guidance stage using the maximum principle L.S. Pontryagin. It is assumed that the spacecraft is equipped with a longitudinal propulsion system running on chemical fuel. The programs  of optimal change in the second fuel consumption and the vector of cosine guides, which determine the orientation of the thrust force of the propulsion system, should be determined. As a criterion for optimal control, we consider a functional that determines the minimum consumption of the working fluid. The optimal control problem is solved in a limited region of the state space, which is determined by the range of variation of the angular range of the spacecraft within one revolution. The full equations of the boundary value problem of the maximum principle are given using the model of the object's motion in the normal gravitational field of the Earth, the boundary conditions, and also the analytical dependencies that determine the control structure in the optimal mode. The boundary optimization problem is solved with the Newton method. To determine the initial approximation of conjugate variables, an analytical solution is given to the problem of energy-optimal approach control in a uniform central field. The results of numerical studies of energy-optimal programs to control the interception in the normal gravitational field of the Earth with the final pitch at the stage of long-range guidance are presented. In general, the use of optimal approach control algorithms in the airborne and ground complex allows to reduce fuel costs when performing the maneuver, reduce time, and expand the reachability area of the target objects. In addition, the optimal solution can be considered as a reference, with which it is necessary to compare various variants of approximate control algorithms, evaluate their quality and make informed decisions on their practical use.
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来源期刊
SPIIRAS Proceedings
SPIIRAS Proceedings Mathematics-Applied Mathematics
CiteScore
1.90
自引率
0.00%
发文量
0
审稿时长
14 weeks
期刊介绍: The SPIIRAS Proceedings journal publishes scientific, scientific-educational, scientific-popular papers relating to computer science, automation, applied mathematics, interdisciplinary research, as well as information technology, the theoretical foundations of computer science (such as mathematical and related to other scientific disciplines), information security and information protection, decision making and artificial intelligence, mathematical modeling, informatization.
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