Three‐Dimensional Guidance Law Design Under Spatial–Temporal Constraints Based on Predefined‐Time Convergence Theory

ABSTRACT To address the interception problem of maneuvering targets with spatial–temporal constraints, this paper develops a three‐dimensional (3D) guidance law based on a novel logarithmic predefined‐time convergence theory and the predefined‐time extended state observer (PTESO). Notably, the paper treats both the convergence time of LOS angle error and the time‐to‐go as regulatory parameters, and prescribes them independently. First, the predefined‐time stability theory for nonlinear systems is established, and a novel logarithm‐based radially unbounded Lyapunov function is constructed to accelerate system state convergence. Relying on this theory, a predefined‐time guidance law along the LOS is derived to guarantee interception against maneuvering targets at a predefined impact time. Next, the paper designs a new predefined‐time sliding mode surface and the corresponding reaching law using predefined‐time sliding mode control (PTSMC) theory. Then, a normal LOS guidance law is proposed, which enforces the LOS angle to strictly converge to the desired value at the specified interception instant. In addition, target maneuvers are treated as disturbances, and a PTESO is constructed to enhance the guidance system's robustness and interception precision. Finally, the paper conducts a detailed stability analysis of the proposed approach via Lyapunov stability theory. Numerical simulations under diverse initial conditions verify the effectiveness and superiority of the presented guidance strategy.