Finite-time differential games in missile guidance: Achieving motion camouflage and robust cooperative encirclement guidance

In this article, a three-dimensional (3D) cooperative interception guidance strategy is proposed, in which multiple missiles encircle a maneuvering target within a leader–follower framework. A cooperative encirclement guidance law is developed by integrating Motion Camouflage (MC) theory, Finite-Time Differential Game (FTDG) theory, and Adaptive Time-Varying Sliding Mode Control (ATVMSMC). The missile closest to the target is designated as the leader. An FTDG-based guidance strategy is formulated using MC theory and differential game analysis to minimize the target’s probability of escape. The finite-time Nash equilibrium solution is derived through a state-dependent differential Riccati equation framework, ensuring that the leader achieves motion camouflage. In scenarios where actuator failures may occur in the followers, a robust cooperative encirclement guidance law is designed based on the leader’s remaining interception time. The ATVMSMC law guarantees that all followers complete the encirclement at the moment of the leader’s interception. The stability of the game-based guidance strategy is verified using Lyapunov theory. Numerical simulations under multiple scenarios demonstrate the effectiveness, robustness, and advantages of the proposed method for cooperative encirclement in pursuit–evasion engagements.