How to do comparative dynamics on the back of an envelope for open-loop Nash equilibria in differential game theory

2016 ◽  
Vol 38 (3) ◽  
pp. 443-458 ◽  
Author(s):  
Michael R. Caputo ◽  
Chen Ling
Keyword(s):  
Game Theory ◽  
Differential Game ◽  
Nash Equilibria ◽  
Open Loop ◽  
Comparative Dynamics ◽  
Differential Game Theory

scholarly journals Evasion-Pursuit Strategy against Defended Aircraft Based on Differential Game Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qilong Sun ◽  
Minghui Shen ◽  
Xiaolong Gu ◽  
Kang Hou ◽  
Naiming Qi
Keyword(s):  
Game Theory ◽  
Differential Game ◽  
Optimal Strategies ◽  
Open Loop ◽  
Active Defense ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Differential Game Theory ◽  
One To One ◽  
The One

The active defense scenario in which the attacker evades from the defender and pursues the target is investigated. In this scenario, the target evades from the attacker, and the defender intercepts the attacker by using the optimal strategies. The evasion and the pursuit boundaries are investigated for the attacker when the three players use the one-to-one optimal guidance laws, which are derived based on differential game theory. It is difficult for the attacker to accomplish the task by using the one-to-one optimal guidance law; thus, a new guidance law is derived. Unlike other papers, in this paper, the accelerations of the target and the defender are unknown to the attacker. The new strategy is derived by linearizing the model along the initial line of sight, and it is obtained based on the open-loop solution form as the closed-loop problem is hard to solve. The results of the guidance performance for the derived guidance law are presented by numerical simulations, and it shows that the attacker can evade the defender and intercept the target successfully by using the proposed strategy.

Hybrid Method Based on Artificial Potential Field and Differential Game Theory for the UAV Path Planing

2014 ◽  
Vol 687-691 ◽  
pp. 260-264
Author(s):  
Feng Tian ◽  
Ji Feng Zou ◽  
Tong Zhang
Keyword(s):  
Game Theory ◽  
Differential Game ◽  
Potential Field ◽  
Artificial Potential Field ◽  
Complex Environment ◽  
Pursuit Evasion ◽  
Differential Game Theory ◽  
Evasion Game ◽  
Simulation Results ◽  
Dynamic Path

In this paper, a method of the UAV path planing in the complex environment by using artificial potential field and differential game theory is introduced. This article studies the pursuit evasion game of the dynamic path planing for the UAV. The fly zone of either the pursuer or the evader is divided into two categories, namely the obstacle areas and the obstacle-free areas. So we can use the artificial potential field in the obstacle areas,and we use differential game theory in the obstacle-free areas for the UAV. This method can apply to pursuit-evasion game in the complex environment for the UAV path planing.Not only the UAV can avoid obstacles but also they can find the best capture path.Finally,the simulation results verify its correctness and validity .

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