• Control Theory and Application •

### Differential game strategy in three-player evasion and pursuit scenarios

Qilong SUN1(), Naiming QI1,*(), Longxu XIAO2(), Haiqi LIN1()

1. 1 Department of Aerospace Engineering, Harbin Institute of Technology, Harbin 150001, China
2 The Rocket Force Equipment Academy, Beijing 100096, China
• Received:2017-02-23 Online:2018-04-26 Published:2018-04-27
• Contact: Naiming QI E-mail:sunqilong27@163.com;qinaimingok_hit@163.com;xlxx@sina.com;linhaiqi_hit@163.com
• About author:SUN Qilong was born in 1989. He is a Ph.D. candidate at Harbin Institute of Technology. He received his B.S. and M.S. degrees in Harbin Institute of Technology in 2012 and 2014, respectively. His research interests are vehicle guidance and control and the dynamics and control of motorized momentum exchange tether systems. E-mail: sunqilong27@163.com|QI Naiming was born in 1963. He received his B.S. and M.S. degrees in Harbin Institute of Technology. He is a professor and Ph.D. supervisor at Harbin Institute of Technology. He is a committee member of the national gas lubrication. His research interests are vehicle guidance and control and mechanical and electrical integration of vehicles. E-mail:qinaimingok_hit@163.com|XIAO Longxu was born in 1962. He received his B.S. degree from the Second Artillery Engineering College in 1982. Currently, he is a professor, Ph.D. supervisor, and chief engineer. He is a director of the Institute of China Aerospace. His main research interests are missile configuration and missile development demonstration and practical operation. E-mail: xlxx@sina.com|LIN Haiqi was born in 1993. He is an M.S. candidate at Harbin Institute of Technology. His research interests are vehicle guidance and control and the dynamics and mechanical and electrical integration of vehicles. E-mail: linhaiqi_hit@163.com
• Supported by:
the National Natural Science Foundation of China(11672093);This work was supported by the National Natural Science Foundation of China (11672093)

Abstract:

A conflict of three players, including an attacker, a defender, and a target with bounded control is discussed based on the differential game theories in which the target and the defender use an optimal pursuit strategy. The current approach chooses the miss distance as the outcome of the conflict. Different optimal guidance laws are investigated, and feasible conditions are analyzed for the attacker to accomplish an attacking task. For some given conditions, the attacker cannot intercept the target by only using a one-to-one optimal pursuit guidance law; thus, a guidance law for the attacker to reach a critical safe value is investigated. Specifically, the guidance law is divided into two parts. Before the engagement time between the defender and the attacker, the attacker uses this derived guidance law to guarantee that the evasion distance from the defender is safe, and that the zero-effort-miss (ZEM) distance between the attacker and the target is the smallest. After that engagement time, the attacker uses the optimal one-toone guidance law to accomplish the pursuit task. The advantages and limited conditions of these derived guidance laws are also investigated by using nonlinear simulations.