Abstract. A differential game of several players is considered as follows. One player (attacker) penetrates some space, and several other players (pursuers) appear simultaneously to intercept the attacker. Upon detecting the pursuers, the attacker tries to evade them. The dynamics of each player are described by a time-invariant linear system of a general type with scalar control. A quadratic functional is introduced, and the differential game is treated as an optimal control problem. Two subproblems are solved as follows. The first subproblem is to construct a strategy for pursuing the attacker by several players who have complete equal information about the game. The second subproblem is to construct such a strategy under incomplete information about the attacker who is actively opposing the pursuers. The simulation results are presented. The zero-sum differential game solution can be used for studying the final stage of pursuit, in which several pursuers and one evader participate.
Keywords: differential games, linear dynamics, optimal feedback control, Nash equilibrium, Lyapunov functions, Riccati equation.
Funding. This work was supported by the Russian Foundation for Basic Research, project no. 19-8-00535.
Afanas’ev, V.N., Semion, A.A. Differential Games of Pursuit with Several Pursuers and One Evader. Control Sciences 1, 21–30 (2021). http://doi.org/10.25728/cs.2021.1.3