Prediction and control of projectile impact point using approximate statistical moments

Abstract

In this thesis, impact point and trajectory control for a projectile are studied. It is vital to have error-free control in order to avoiding hitting protected areas, e.g. schools and hospitals. This limitation makes projectile analysis, and controller design more difficult. Projectiles are subject to environmental noise such as wind effect and transmission channels that are corrupted by the enemy. Moreover, the number of parameters and states in the projectile mathematical models significantly large when the realistic prediction is taken into account because of the effects of natural forces and moments. In addition, projectile dynamics have nonlinear functions such as monomials and sine functions. To address all these issues, a model which reduces the size, and contains randomness is formulated for the projectile. In this model, nonlinear functions are converted of the form of monomials. Then, approximated moment dynamics is described by using mean-field approximation. The suggested method in this thesis still suffers from the size of the system. To solve this size problem, a subset of first- and second-order statistical moments are chosen to have reliable approximations of the mean and standard deviation of the impact point for a real projectile. In the last chapters, these selected moments are used to derive a control law such as first order moment as the desired trajectory. This law guarantees to hit a target with minimum error.