Bounded Linear-Quadratic Differential Game Guidance Law for Dual-Thruster Controlled Missiles

Abstract

A guidance law tailored for an interceptor missile steered by aerodynamic lift and divert-thruster and with its attitude oriented by forward attitude-thruster (dual-thruster control) is proposed. The bang-bang strategy has the maximal capture zone. However, it leads to control chattering, resulting in excessive control effort. The continuous strategies have smaller capture zones, but can require a smaller control effort. The combination of bang-bang and continuous strategies may lead to a cooperative effect of the capture zone and control effort. In this paper, the guidance law is derived using a linear-quadratic differential game formulation and then modified for bounded controls. For the derivation, the interceptor closed-loop dynamics is represented by a first-order biproper transfer function for the attitude-thruster control system and a strictly proper one for the divert-thruster control system, respectively. Analysis based on the proposed guidance law shows that the divert-thruster control system has higher efficiency due to its small time constant and the direct forces that mainly affect the short-term behavior of the missiles. The parameters’ effects and the control command distribution are also studied.