Optimality of Linear Time-Varying Guidance for Impact Angle Control

Abstract

The work presented here demonstrates optimality of linear time-varying guidance laws for controlling impact angles as well as terminal misses using the inverse problem of optimal control theory. Under the assumptions of a stationary target and a lag-free missile with a constant speed and a small flight path angle, it is shown that a generalized linear time-varying guidance law with an arbitrary pair of guidance coefficients can minimize a certain quadratic performance index subject to the terminal constraints. Feasible sets of the guidance coefficients for capturability are investigated and explicitly stated by yielding the closed-form solutions of the guidance loop in this paper. These results imply that it is possible for more realistic settings of the guidance coefficients either to improve the guidance performance or to achieve some specific guidance objectives in practical environments. Furthermore, the time-to-go calculation methods, which consider the closed-loop solutions for arbitrary guidance coefficients, are included for implementation of the guidance law. Linear and nonlinear simulations are performed to validate the proposed approach.