Initial states iterative learning for three-dimensional ballistic endpoint control

In this paper, an initial states iterative learning control algorithm is proposed for control of the ballistic endpoint displacement in three-dimensional space, where the target is moving and the projectile experiences system uncertainties. The characteristics of the three-dimensional ballistic process are formulated and explored, and the learning algorithm is proposed in the spatial domain. The algorithm consists of two parts. First, the initial speed and angles are iteratively learned to make the projectile attain a fixed position. Second, the shooting time is learned to tune the arrival time of the projectile. Since the dimensions of the solution space are larger than that of the task space, three control manners, including shooting speed, shooting angle and their combination, are researched respectively. Through rigorously analyzed, it is proved that the algorithm is convergent and the multiple initial states can be adjusted simultaneously. Finally, an example of practical cannonball projection is presented to verify the effectiveness of the proposed algorithms.