Three-dimensional nonlinear H_∞ guidance law

This paper proposes a novel three-dimensional missile guidance law design based on nonlinear H_∞ control. The complete nonlinear kinematics of pursuit-evasion motion is considered in the three-dimensional spherical co-ordinates system; neither linearization nor small angle assumption is made here. The nonlinear H_∞ guidance law is expressed in a simple form by solving the associated Hamilton-Jacobi partial differential inequality analytically. Unlike adaptive guidance laws, the implement of the proposed robust H_∞ guidance law does not require the information of target acceleration, while ensuring acceptable interceptive performance for arbitrary target with finite acceleration. The resulting pursuit-evasion trajectories for both the H_∞-guided missile and the worst-case target are determined in closed form, and the performance robustness against variations in target acceleration, in engagement condition, and in control loop gain, is verified by numerical simulations.