Finite energy reachable set and its optimal ellipsoid approximations in relative orbital dynamics

IF 5 1区工程技术 Q1 ENGINEERING, AEROSPACE

Aerospace Science and Technology Pub Date : 2025-04-01 DOI:10.1016/j.ast.2025.110188

Jianye Sun, Dong Ye, Yan Xiao

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Abstract

To prevent distortions in estimation caused by abnormal thrust magnitudes, finite energy reachable sets are essential for estimating the maximum state range of a spacecraft during engine failures. This paper examines finite energy reachable sets defined by a combination of initial state sets and weighted energy constraints. Through rigorous mathematical proofs, it is demonstrated that the reachable boundaries form the union of several convex sets. Due to the computational complexity involved in determining the envelope of this union, which poses challenges for real-time engineering applications, an equivalent transformation of the finite energy reachable set into the Minkowski sum of the initial state gain set and the control gain set is proposed. Recognizing the lower computational power of space-grade processors compared to personal computers, this paper develops optimal trace inner and outer ellipsoid approximations of the ellipsoidal Minkowski sum, avoiding reliance on matrix eigenvalue computations through matrix analysis. The result is a significant improvement in the accuracy of the approximate solution with comparable efficiency.

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来源期刊

Aerospace Science and Technology 工程技术-工程：宇航

CiteScore

10.30

自引率

28.60%

发文量

654

审稿时长

54 days

期刊介绍： Aerospace Science and Technology publishes articles of outstanding scientific quality. Each article is reviewed by two referees. The journal welcomes papers from a wide range of countries. This journal publishes original papers, review articles and short communications related to all fields of aerospace research, fundamental and applied, potential applications of which are clearly related to: • The design and the manufacture of aircraft, helicopters, missiles, launchers and satellites • The control of their environment • The study of various systems they are involved in, as supports or as targets. Authors are invited to submit papers on new advances in the following topics to aerospace applications: • Fluid dynamics • Energetics and propulsion • Materials and structures • Flight mechanics • Navigation, guidance and control • Acoustics • Optics • Electromagnetism and radar • Signal and image processing • Information processing • Data fusion • Decision aid • Human behaviour • Robotics and intelligent systems • Complex system engineering. Etc.