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A design method of differential game guidance law based on Dubins path and neural network

Published online by Cambridge University Press:  10 October 2025

B. M. Liu Open the ORCID record for B. M. Liu [Opens in a new window] ,
Z. X. Zhu Open the ORCID record for Z. X. Zhu [Opens in a new window] ,
Z. Zhu  and
Z. X. Pan
B. M. Liu
Affiliation:
National Key Laboratory of Aerospace Flight Dynamics, Xi’an, China School of Astronautics, Northwestern Polytechnical University, Xi’an, China
Z. X. Zhu*
Affiliation:
National Key Laboratory of Aerospace Flight Dynamics, Xi’an, China School of Astronautics, Northwestern Polytechnical University, Xi’an, China
Z. Zhu
Affiliation:
National Key Laboratory of Aerospace Flight Dynamics, Xi’an, China School of Astronautics, Northwestern Polytechnical University, Xi’an, China
Z. X. Pan
Affiliation:
National Key Laboratory of Aerospace Flight Dynamics, Xi’an, China School of Astronautics, Northwestern Polytechnical University, Xi’an, China
*
Corresponding author: Z. X. Zhu; Email: zhuzhanxia@nwpu.edu.cn
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Abstract

This study proposes a geometric solution to the norm differential game design problem in target-attacker-defender (TAD) engagements, addressing key limitations of conventional zero-effort-miss approaches. By leveraging the geometric analogy between guidance-law-generated trajectories and Dubins paths, we reformulate the derivation of zero-effort-miss-based guidance laws as a Nash equilibrium optimisation problem, with optimal strategies determined through reachable set analysis of Dubins path frontier. The resulting model is a non-convex optimisation problem, which prevents the derivation of traditional state-feedback control laws. To overcome this limitation and enable real-time implementation, we develop a custom back propagation neural network, enhanced with a relaxation factor method for output filtering, a Holt linear trend model for outlier compensation and a saturation function for oscillation suppression. Extensive simulations demonstrate that the proposed framework significantly outperforms baseline methods. These results validate the effectiveness and robustness of our approach for high-performance TAD applications.

Keywords

BP neural networkDubins pathDP-NNDGnorm differential game

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Type
Research Article
Information
The Aeronautical Journal , First View , pp. 1 - 21
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Royal Aeronautical Society

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