Backstepping Guidance for Missiles Modeled as Uncertain Time-Varying First-Order Systems

This paper proposes a Lyapunov-based guidance law, which takes into account the nonlinear relative kinematics between the missile and the target, and ensures ultimate boundedness of the missile-target system trajectories provided the estimation error of the target acceleration is bounded in magnitude. The proposed guidance synthesis, which combines high-gain backstepping and variable structure approach, takes into account the uncertain flight control dynamics. Numerical simulations of the proposed guidance in closed-loop with an interval 2nd-order missile transfer function and a maneuvering target demonstrate satisfactory performances when compared to several other modern and classical guidance laws. Furthermore, it is shown that using the estimate of the target acceleration in the guidance allows achieving a relatively small miss distance when the pursuer-evader maximum maneuverability ratio approaches unity. However, the satisfactory performance comes at the expense of a stringent acceleration demand in the early part of the engagement, which is typical of high-gain control.