Game of Defending a Target: A Linear Quadratic Differential Game Approach

Abstract Pursuit-evasion (PE) differential games have recently received much attention in military applications involving adversaries. We extend the PE game problem to a problem of defending target, where the roles of the players are changed. The evader is to attack some fixed target, whereas the pursuer is to defend the target by intercepting the evader. We propose a practical strategy design approach based on the linear quadratic game theory with a receding horizon implementation. We prove the existence of solutions for the Riccati equations associated with games with simple dynamics. Simulation results justify the method.

[1]  Alexandre M. Bayen,et al.  A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games , 2005, IEEE Transactions on Automatic Control.

[2]  Dongxu Li,et al.  Improvement with Look-ahead on Cooperative Pursuit Games , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[3]  S. Sastry,et al.  Probabilistic pursuit-evasion games: a one-step Nash approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[4]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[5]  Josef Shinar,et al.  Missile guidance laws based on pursuit-evasion game formulations , 2003, Autom..

[6]  M. Pachter.  SIMPLE-MOTION PURSUIT–EVASION IN THE HALF PLANE , 1987 .

[7]  P. Souganidis,et al.  Differential Games and Representation Formulas for Solutions of Hamilton-Jacobi-Isaacs Equations. , 1983 .

[8]  Yong Liu,et al.  Pop-up threat models for persistent area denial , 2007, IEEE Transactions on Aerospace and Electronic Systems.

[9]  G. Jank,et al.  Existence and comparison theorems for algebraic Riccati equations and Riccati differential and difference equations , 1996 .

[10]  Y. Ho,et al.  Differential games and optimal pursuit-evasion strategies , 1965 .

[11]  Dongxu Li,et al.  Stochastic multi‐player pursuit–evasion differential games , 2008 .

[12]  R. Isaacs.  Differential games: a mathematical theory with applications to warfare and pursuit , 1999 .

[13]  Prasanta K. Bose,et al.  Swarm Coordination for Pursuit Evasion Games using Sensor Networks , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[14]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[15]  Jacob Engwerda,et al.  LQ Dynamic Optimization and Differential Games , 2005 .