Multiple Pursuer Multiple Evader Differential Games

• Published in: IEEE transactions on automatic control Vol. 66; no. 5; pp. 2345 - 2350
• Main Authors: Garcia, Eloy, Casbeer, David W., Von Moll, Alexander, Pachter, Meir
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aerospace electronics; Autonomous systems; Co-design; Differential games; Game theory; Games; Government; intelligent control; optimal control; Pursuit-evasion games; Saddle points; State feedback; Switches; Teams; Weapons
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3003840

In this article an <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula>-pursuer versus <inline-formula><tex-math notation="LaTeX">M</tex-math></inline-formula>-evader team conflict is studied. This article extends classical differential game theory to simultaneously address weapon assignments and multiplayer pursuit-evasion scenarios. Saddle-point strategies that provide guaranteed performance for each team regardless of the actual strategies implemented by the opponent are devised. The players' optimal strategies require the codesign of cooperative optimal assignments and optimal guidance laws. A representative measure of performance is employed and the Value function of the attendant game is obtained. It is shown that the Value function is continuously differentiable and that it satisfies the Hamilton-Jacobi-Isaacs equation-the curse of dimensionality is overcome and the optimal strategies are obtained. The cases of <inline-formula><tex-math notation="LaTeX">N=M</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">N>M</tex-math></inline-formula> are considered. In the latter case, cooperative guidance strategies are also developed in order for the pursuers to exploit their numerical advantage. This article provides a foundation to formally analyze complex and high-dimensional conflicts between teams of <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula> pursuers and <inline-formula><tex-math notation="LaTeX">M</tex-math></inline-formula> evaders by means of differential game theory.