Abstract
We consider optimal two-impulse space interception problems with multiple constraints. The multiple constraints are imposed on the terminal position of a space interceptor, impulse and impact instants, and the component-wise magnitudes of velocity impulses. These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations. Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used. A new dynamic slackness variable method is presented. As a result, an indirect optimization method is developed. Subsequently, our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles. A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions. Specifically, by numerical examples, we show that when time and velocity impulse constraints are imposed, optimal two-impulse solutions may occur; if two-impulse instants are free, then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.
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Acknowledgements
We appreciate Prof. PRUSSING and Dr. SANDRIK for sharing their MATLAB scripts in Sandrik (2006). Also, thank Dr. KIERZENKA, one of the authors of these MATLAB boundary value problem solvers, for sending us his PhD dissertation (Kierzenka, 1998). We appreciate the MATLAB solvers, and without them we do not have this work.
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Li XIE, Yi-qun ZHANG, and Jun-yan XU declare that they have no conflict of interest.
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Project supported by the National Natural Science Foundation of China (No. 61374084)
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Xie, L., Zhang, Yq. & Xu, Jy. Optimal two-impulse space interception with multiple constraints. Front Inform Technol Electron Eng 21, 1085–1107 (2020). https://doi.org/10.1631/FITEE.1800763
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DOI: https://doi.org/10.1631/FITEE.1800763
Key words
- Space interception problems
- Variational method
- Multiple constraints
- Two-velocity impulses
- Multi-point boundary value problems
- Local optimal solutions
- Dynamic slackness variable method