3D Nonlinear $H_2$/$H_1$ Guidance Law

Abstract

In this paper, a three-dimensional (3D) nonlinear guidance design based on $H_2$/$H_1$ criteria is proposed for homing missile system. Full 3D nonlinear motions in spherical coordinate are considered without any linearization. The design objective is to synthesize a robust guidance law against arbitrary target maneuvers by making use of nonlinear $H_1$ approach, while satisfying a nonlinear quadratic ($H_2$) performance constraint. This $H_2$/$H_1$ formulation of guidance problems leads to two coupled Hamilton-Jacobi partial differential inequality (HJPDI). It is shown that the coupled HJPDIs possess a simple analytical solution from which a closed-form expression of the nonlinear $H_2$/$H_1$ guidance law can be derived. The performance of the $H_2$/$H_1$ guidance law is veriffied in a missile-to-aircraft combat simulation where the optimal discrete game theory is used to generate an intelligent maneuvering target and a practical scoring system is applied to evaluate the resulted missile-to-aircraft combat.