Three-body cooperative active defense guidance law with overload constraints: A small speed ratio perspective

In air combat, one effective way to counter an incoming missile attacking an aircraft is to launch a defense missile compared with traditional passive defense strategies such as decoy and electronic countermeasures. To address this issue, this paper proposes a three-body cooperative active defense guidance law with overload constraints from the perspective of a small speed ratio. First, a cooperative guidance-oriented model for active defense is established and linearized to provide a foundation for the design of the guidance law. Then, the essential quantity known as Zero-Effort-Miss (ZEM) is analyzed during the engagement process. In order to minimize the influence of inaccurate estimates of remaining flight time in the ZEM, the concept of Zero-Effort-Velocity (ZEV) is introduced. Subsequently, utilizing the sliding mode control method, the guidance law is designed by selecting the ZEM and ZEV as sliding mode surfaces, combined with the fast power reaching law, and its finite-time stability is analyzed using the Lyapunov method. Furthermore, to quantitatively evaluate the performance of the proposed active defense guidance law, the interception rendezvous angle index is introduced. The proposed active defense guidance law considers integrating information from the incoming missile, aircraft, and defense missile with fewer simplifications and assumptions, and ensures that the aircraft is effectively protected with less overload required for the defense missile. Finally, simulation experiments demonstrate the effectiveness and adaptability of the proposed active defense guidance law.