Three-Dimensional Guidance Law with LOS Angle and Attack Lead Angle Constraints Based on Predefined-Time Control Theory

Considering the LOS (line of sight) angle and the attack lead angle constraints, a novel guidance law based on predefined-time convergence theory and the concept of DSC (dynamic surface control) is proposed for intercepting the maneuvering target in this paper. In contrast to existing guidance laws, the proposed guidance law allows the convergence time of the impact angle error to be preset by the designer, and it is independent of the system’s initial states. First, the paper introduces the predefined-time stability theory of nonlinear systems and constructs a novel radially unbounded Lyapunov candidate based on the natural logarithm, thereby ensuring system states convergence within predefined time. Then the mapping between the attack lead angle and the LOS angle is established to ensure their simultaneous convergence. Leveraging this relationship, a novel guidance law is designed by integrating predefined-time control theory with the DSC methodology. The proposed law guarantees that the impact angle error converges to zero within a predefined_-time. Finally, a detailed Lyapunov stability analysis is presented for the overall predefined-time convergent guidance system. At last, several simulation cases are carried out to illustrate the effectiveness of the proposed guidance law.