Lyapunov-Based Guidance Law for Impact Time Control and Simultaneous Arrival

A new Lyapunov-based guidance law with an exact expression for impact time is presented. The impact time is derived in terms of a beta function of the initial heading error and can be controlled by varying a single parameter. The minimum and maximum impact times are derived based on the initial engagement geometry. Lateral acceleration characteristics are analyzed, presenting a monotonically decreasing command with an analytic bound on maximum value. A feedback form of the guidance law is presented for implementation with uncompensated autopilot dynamics. The simulation results present negligible impact time errors for autopilot first-order time constants as high as 0.4 s. The simulation results validate the analytic findings.