Multiple Constraints-Based Adaptive Three-Dimensional Back-Stepping Sliding Mode Guidance Law against a Maneuvering Target

Abstract

This paper addresses the issue of a complex three-dimension (3-D) terminal guidance process that is used against maneuvering targets while considering both the terminal impact angle (TIA) and field-of-view (FOV) angle constraints. According to the highly coupled and nonlinear 3-D terminal guidance model, an adaptive back-stepping sliding-mode guidance law algorithm is proposed in order to guarantee the stability and robustness of the guidance system. Considering the explicit expression of the line-of-sight (LOS) angle in the kinematics and dynamics of the terminal guidance process, the TIA constraint is transformed into an LOS constraint based on their well-known relationship. In view of the challenges in obtaining the motion information of maneuvering targets, an adaptive law design is introduced in order to estimate and compensate for external disturbances caused by the maneuvering of the target and modeling uncertainty. In addition, because the FOV angle represented by the overall leading angle is not a state variable in the sliding-mode guidance system, it is decoupled into two partial leading angles based on a specific transformation relation, so the 3-D terminal guidance control problem is converted into separate tracking system control issues in the pitch and yaw planes. Then, the Lyapunov stability theory is utilized to substantiate the stability of the guidance system, where the Lyapunov functions in both of the subsystems consist of the LOS and partial FOV state error terms. Finally, a series of simulations of various motion states of maneuvering targets under different terminal cases were carried out. It was proved that the terminal guidance design based on the strategies presented above was able to obtain the desired LOS constraints with satisfying the FOV limitation, and the simulation results verified the effectiveness, universality, and significance for practical applications of the proposed guidance design method.