Variational Calculus Approach to Optimal Interception Task of a Ballistic Missile in 1D and 2D Cases

Dariusz Horla

doi:10.3390/a12080148

Abstract

The paper presents the application of variational calculus to achieve the optimal design of the open-loop control law in the process of anti-ballistic missile interception task. It presents the analytical results in the form of appropriate Euler–Lagrange equations for three different performance indices, with a simple model of the rocket and the missile, based on the conservation of momentum principle. It also presents the software program enabling rapid simulation of the interception process with selected parameters, parametric analysis, as well as easy potential modification by other researchers, as it is written in open code as m-function of Matlab.

Highlights

Interception of ballistic missiles has been a research topic for years
The paper [1] employs the proposed guidance law in real-world conditions, where interception trajectories are sought in R6, comprising of: three NED coordinates, speed, path angle and heading of the interceptor
The functional may refer to flight time of the intercepting missile, or distance between the interceptor and the ballistic missile

Summary

Introduction

The paper [1] employs the proposed guidance law in real-world conditions, where interception trajectories are sought in R6 , comprising of: three NED (north-east-down) coordinates, speed, path angle and heading of the interceptor. This usually calls for the use of optimization techniques to obtain the reference trajectories to follow. The functional may refer to flight time of the intercepting missile, or distance between the interceptor and the ballistic missile. Guidance of an intercepting rocket is a problem which has multiple solutions. One can distinguish passive and active guidance approaches [4].

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Conclusion