In the guidance law capturability analysis, the differential game theory is complemented by considering the optimal situation for both the evader and the pursuer as the capture boundary, and it is commonly used to derive the necessary and sufficient conditions of capture zones. However, in previous studies, capturability was analyzed for continuous guidance laws. Still, pulsed guidance laws, which are sometimes used in reality, such as pulsed orbital thrust control for exo-atmospheric vehicles, have different capture zones and influence factors.
To address the above-mentioned challenge, a team of automation scientists led by Professor Qinglei Hu from the School of Automation Science and Electrical Engineering at Beihang University, China, recently derived the capture zones of the pulsed and the continuous guidance laws for both the pursuer and the evader, and theoretically discussed their differences and influence factors. Specifically, the boundary of the initial zero miss distance between the capture zone and the non-capture zone regarding the pulsed guidance law and the continuous guidance law was generated in a unified form.
"In this study, the distinction between the pulsed guidance law and the continuous guidance law and their impact on capture zones are revealed. The obtained capturability analysis results are user/designer-friendly to provide a theoretical guideline for the guidance law selection in various continuous and pulsed pursuit-evasion games regarding different acceleration ratios and time constant ratios," said Qinglei Hu.
The team published their work in the Chinese Journal of Aeronautics on May 20, 2025.
According to their work, if the optimal solution exists, for the pursuer, the distinction of the pulsed and continuous guidance laws can be neglected with a small guidance effort weight, and the capture zone of the continuous guidance law is larger than the pulsed guidance law with a large guidance effort weight. For the evader, the distinction between the pulsed and the continuous guidance laws can be neglected with small guidance effort weight, but the capture zone of the pulsed guidance law is larger than the continuous guidance law with large guidance effort weight.
Therefore, in the guidance law design process, the pulsed guidance law could be treated as the continuous guidance law with small guidance effort weights, where the slight difference in the corresponding capture zone could be neglected. However, with large guidance effort weights, the differences could not be neglected, where the capture zone of the continuous guidance law is larger than the pulsed guidance law with large pursuer guidance effort weight, but smaller with large evader guidance effort weight. Moreover, to capture the evader, the pursuer could choose a smaller guidance effort weight, a higher time constant ratio, and a higher acceleration ratio, whereas the evader could choose a smaller guidance effort weight, a smaller time constant ratio, and a smaller acceleration ratio to escape from the pursuer.
Other contributors include Yuting Lu, Yang Yu, Tuo Han, Jianying Zheng from the School of Automation Science and Electrical Engineering at Beihang University in Beijing, China; Tianmushan Laboratory in Hangzhou, China; and Hangzhou International Innovation Institute at Beihang University in Hangzhou, China.
Original Source
Yuting Lu, Qinglei Hu, Yang Yu, Tuo Han, Jianying Zheng. Capturability distinction analysis of continuous and pulsed guidance laws [J]. Chinese Journal of Aeronautics, 2025, https://doi.org/10.1016/j.cja.2025.103579.
About Chinese Journal of Aeronautics
Chinese Journal of Aeronautics (CJA) is an open access, peer-reviewed international journal covering all aspects of aerospace engineering, monthly published by Elsevier. The Journal reports the scientific and technological achievements and frontiers in aeronautic engineering and astronautic engineering, in both theory and practice. CJA is indexed in SCI (IF = 5.7, Q1), EI, IAA, AJ, CSA, Scopus.
