# Fractional Calculus Guidance Algorithm in a Hypersonic Pursuit-Evasion Game

• Jian Chen College of Engineering, China Agricultural University, Beijing -100 083
• Qilun Zhao School of Automation Science and Electrical Engineering, Science and Technology on Aircraft Control Laboratory, Beihang University, Beijing - 10 0191
• Zixuan Liang School of Automation Science and Electrical Engineering, Science and Technology on Aircraft Control Laboratory, Beihang University, Beijing - 10 0191
• Peng Li Department of Mechanical Engineering, University of Houston, Houston - 77 204
• Zhang Ren School of Automation Science and Electrical Engineering, Science and Technology on Aircraft Control Laboratory, Beihang University, Beijing - 10 0191
• Yongjun Zheng College of Engineering, China Agricultural University, Beijing -100 083
Keywords: Pursuit-evasion game, Target manoeuver, Fractional calculus, Guidance law, Hypersonic weapon

### Abstract

Aiming at intercepting a hypersonic weapon in a hypersonic pursuit-evasion game, this paper presents a fractional calculus guidance algorithm based on a nonlinear proportional and differential guidance law. First, under the premise of without increasing the complexity degree of the guidance system against a hypersonic manoeuvering target, the principle that the differential signal of the line-of-sight rate is more sensitive to the target manoeuver than the line-of-sight rate is employed as the guidelines to design the guidance law. A nonlinear proportional and differential guidance law (NPDG) is designed by using the differential derivative of the line-of-sight rate from a nonlinear tracking differentiator. By using the differential definition of fractional calculus, on the basis of the NPDG, a fractional calculus guidance law (FCG) is proposed. According to relative motions between the interceptor and target, the guidance system stability condition with the FCG is given and quantitative values are also proposed for the parameters of the FCG. Under different target manoeuver conditions and noisy conditions, the interception accuracy and robustness of these two guidance laws are analysed. Numerical experimental results demonstrate that the proposed guidance algorithms effectively reduce the miss distance against target manoeuvers. Compared with the NPDG, a stronger robustness of the FCG is shown under noisy condition.

### Author Biographies

Jian Chen, College of Engineering, China Agricultural University, Beijing -100 083

Dr Jian Chen received the BS and PhD in guidance, navigation and control from Beihang University, Beijing, China. He is currently an Associate Professor (PhD Advisor) with the College of Engineering, China Agricultural University, Beijing, China. Before that, he was a research scientist in ASM Technology Limited, Hong Kong, China. And he held the post of research fellows in University of Houston, USA, and University of Toronto, Canada. His current research interests include guidance, navigation and control of UAVs and robotics.

Contribution in the current study is design, deduction and stability proof of the fractional calculus guidance law for intercepting hypersonic targets.

Qilun Zhao, School of Automation Science and Electrical Engineering, Science and Technology on Aircraft Control Laboratory, Beihang University, Beijing - 10 0191

Mr Qilun Zhao received the BS in automation from Nanjing University of Science and Technology, Nanjing, China. He is currently a PhD candidate with the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. His current research interests include guidance, navigation and control of hypersonic vehicles.

In the present study he has conducted part of hypersonic-interception simulations.

Zixuan Liang, School of Automation Science and Electrical Engineering, Science and Technology on Aircraft Control Laboratory, Beihang University, Beijing - 10 0191

Dr Zixuan Liang received the BS and PhD in guidance, navigation and control from Beihang University, Beijing, China. He is currently a Postdoctoral Research Fellow with the School of Astronautics, Beihang University. His current research interests include guidance, navigation and control of hypersonic vehicles.

In the present study he has provided characteristics analysis of hypersonic vehicles.

Peng Li, Department of Mechanical Engineering, University of Houston, Houston - 77 204

Dr Peng Li received the BSand MSin guidance, navigation and control from Beihang University, Beijing, China. He received the PhD in mechatronics engineering from University of Houston, USA. His current research interests include robust control and embedded control systems.

In the present study he has conducted part of hypersonic-interception simulations.

Zhang Ren, School of Automation Science and Electrical Engineering, Science and Technology on Aircraft Control Laboratory, Beihang University, Beijing - 10 0191

Dr Zhang Ren received the BS, MSand PhD in aerospace engineering from Northwest Polytechnical University, Xi’an, China. He is currently a Professor with the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. His current research interests include guidance, navigation and control, fault control systems, and robust control.

In the present study he has provided characteristics analysis of hypersonic vehicles.

Yongjun Zheng, College of Engineering, China Agricultural University, Beijing -100 083

Dr Yongjun Zheng received the BS, MSand PhD in mechanical engineering from China Agricultural University, Beijing, China. He is currently an Associate Professor with the College of Engineering, China Agricultural University. His current research interests include fluid analysis of UAVs and intelligent sensing.

In the present study he has conducted part of hypersonic-interception simulations.

Published
2017-11-06
How to Cite
Chen, J., Zhao, Q., Liang, Z., Li, P., Ren, Z., & Zheng, Y. (2017). Fractional Calculus Guidance Algorithm in a Hypersonic Pursuit-Evasion Game. Defence Science Journal, 67(6), 688-697. https://doi.org/10.14429/dsj.67.10897
Issue
Section
Missile Systems