  The optimal cooperative guidance in the nonlinear setting for intercepting a
target by multiple pursuers is studied in the paper. As certain relative angles
can improve observability, the guidance command is required to cooperatively
control the pursuers to intercept the target with specific relative angles. By
using the neural networks, an approach for real-time generation of the
nonlinear cooperative optimal guidance command is developed. Specifically, the
optimal control problem with constraints on relative intercepting angles is
formulated. Then, Pontryagin's maximum principle is used to derive the
necessary conditions for optimality, which are further employed to parameterize
the nonlinear optimal guidance law. As a result, the dataset for the mapping
from state to nonlinear optimal guidance command can be generated by a simple
propagation. A simple feedforward neural network is trained by the dataset to
generate the nonlinear optimal guidance command. Finally, numerical examples
are presented, showing that a nonlinear optimal guidance command with specific
relative angles can be generated within a faction of a millisecond.
