  In this paper, trajectory prediction and control design for a desired hit
point of a projectile is studied. Projectiles are subject to environment noise
such as wind effect and measurement noise. In addition, mathematical models of
projectiles contain a large number of important states that should be taken
into account for having a realistic prediction. Furthermore, dynamics of
projectiles contain nonlinear functions such as monomials and sine functions.
To address all these issues we formulate a stochastic model for the projectile.
We showed that with a set of transformations projectile dynamics only contains
nonlinearities of the form of monomials. In the next step we derived
approximate moment dynamics of this system using mean-field approximation. Our
method still suffers from size of the system. To address this problem we
selected a subset of first- and second-order statistical moments and we showed
that they give reliable approximations of the mean and standard deviation of
the impact point for a real projectile. Finally we used these selected moments
to derive a control law that reduces error to hit a desired point.
