Optimal Guidance Law with Impact-Angle Constraint and Acceleration Limit for Exo-Atmospheric Interception

Shilei Zhao,Liang Yang,Wanchun Chen

doi:10.3390/aerospace8120358

Abstract

This paper aims to develop an optimal guidance law for exo-atmospheric interception, in which impact-angle constraint and acceleration limit are considered. Firstly, an optimal control problem with constraints on terminal miss and impact-angle is formulated, in which the control energy performance index is weighted by a power function of the time-to-go. The closed-loop guidance command, which is expressed as a linear combination of zero-effort miss distance and the zero-effort angle error, is derived using a traditional order reduction transformation. Then, an analytical solution to the maximal acceleration during the flight is obtained by analyzing the boundary points and critical points of the guidance command curve. It is found that the maximal acceleration is a function of the weighted gain in the performance index. Therefore, the maximal acceleration can be efficiently limited by using the variable weighted gain. Furthermore, the relationship between the total control energy and the weighted gain is studied. As a result, a systematic method is proposed for selecting the weighted gain so as to meet the constraint of the acceleration while the total control energy is minimal. Nonlinear simulations have been carried out to test the performance of the proposed method. The results show that this method performs well in intercepting the maneuvering target with a negligible miss distance and intercept angle error. And it can tolerate a stricter acceleration limit in comparison with the typical method.

Highlights

The terminal guidance law, which has direct influence on kill efficiency, is immensely important for the weapon system
The acceleration limit is another crucial constraint on homing missiles, which will lead to large miss-distance and impact angle error if the acceleration saturation occurs near the target
The results show that this method performs well in intercepting the maneuvering target with the impact angle constraint and acceleration limit

Summary

Introduction

The terminal guidance law, which has direct influence on kill efficiency, is immensely important for the weapon system. In [4], a similar formulation was used to derive a linear quadratic optimal guidance law and linear quadratic differential game-based laws for maneuvering target scenarios. These two formulations can be utilized to impose a terminal intercept angle by selecting the ratio between the relative terminal velocity and the closing speed. Shaferman [10] derived two impact angle control guidance laws based on the optimal control and differential game theory for an evasive maneuvering target. A terminal body angle control guidance law considering the angle-of-attack dynamics was developed in [12]. The terminal acceleration cannot be guaranteed to be zero, which possibly increases the miss-distance

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Results

Conclusion