The Game of Degree of Target-Attacker-Defender Game With Non-zero Capture Radius

In the Target-Attacker-Defender (TAD) game, the Attacker endeavors to seize the Target, as the Defender strives to thwart the Attacker and enable the Target to evade being captured. Typically, the Attacker has a non-zero capture radius and can hit the Target by exploding within a certain area around it. Currently, no optimal feedback strategy exists for the Attacker’s winning region when the Attacker’s speed equals the Defender’s and has a non-zero capture radius. This article addresses this gap by focusing on the TAD game with a non-zero capture radius and deriving the optimal feedback strategy through the Game of Degree analysis. We solved the optimal strategy for the Attacker’s winning region using a two-point boundary value problem and proved that the strategy is established as a state feedback Nash equilibrium. The method’s effectiveness was confirmed through simulations.