Robust Smooth Missile Guidance Law using Lyapunov Theory

This paper presents a smooth and robust missile guidance law that enables a missile to intercept a target despite the presence of unknown inputs such as target maneuvers and disturbances like wind. To address the performance degradation of conventional Proportional Navigation Guidance (PNG) caused by external disturbances and rapid target maneuvering, the proposed design defines a corrected target angle based on the geometric relationship between the missile and target velocity vectors, incorporating the collision triangle concept derived from maritime navigation. By applying Lyapunov stability theory, the proposed design ensures that the error angle converges to zero and provides a guidance law that is robust to uncertainties without the need for a separate disturbance observer. To handle uncertainties arising from unknown target motions and wind effects during the Lyapunov stability derivation, the control input is selected to include a smooth hyperbolic tangent function. Simulation results verify that the proposed guidance law exhibits robust performance, including a significantly reduced miss distance (less than 1m) and stable trajectories, across various target speeds, uncertain maneuvers, and operating conditions.