This paper proposes a two-phase game guidance strategy for the three-body confrontation scenario according to the linear quadratic differential game method, which includes an Attacker, an Interceptor, and a Target. The interception probabilities between the Attacker and the Interceptor-Target team are estimated using the probability density function. The desired zero-effort miss distances associated with the interception probabilities for the three-body conflict are acquired by virtue of the gradient descent method. The game combat is divided into two phases by introducing the switching time. In Phase 1, a differential game strategy is developed to guide the zero-control miss distance between the Attacker and the Interceptor-Target into the desired position, which guarantees that the Attacker has the maximizing probability of intercepting the Target and the minimizing probability of being captured by the Interceptor. In Phase 2, a differential game guidance strategy is proposed to ensure that the Attacker evades the pursuit of the Interceptor and intercepts the Target at the preset impact angle. Finally, numerical simulation verifies the effectiveness of the two-stage game guidance strategy.

A new type of guidance strategy, combining linear quadratic and norm-bounded game theory, is proposed for the scenario of an attacker against active defense aircraft in three-player engagement. The problem involves three players, an attacker, a defender and a target. The differential game theory and the solution of Hamiltonian equation are utilized to obtain the combined guidance strategy for each player with arbitrary-order dynamics. The game process is divided into 4 phases, C1-C4, according to the switching time. The linear quadratic differential game guidance scheme is employed to reduce the fuel cost in the game parts of C1 and C3. The norm-bounded game guidance strategy is adopted to satisfy the constraint of control input in the game stages C2 and C4. Furthermore, zero-effort miss distance is introduced to meet the constraints of game space and defender’s killing radius in the guidance strategy, which guarantees that the attacker is able to avoid the interception of the defender and hit the target with lower fuel cost and maximum acceleration. And it is proved that the proposed guidance strategy satisfies the Nash equilibrium condition. Finally, the feasibility and superiority of combined guidance strategy are respectively illustrated by nonlinear numerical simulation and verified by comparing with linear quadratic and norm-bounded differential game guidance strategies.