For the precise targeting in inertial confinement fusion (ICF), the requirements for beam transformation, beam shaping and beam control are harsh. The digital control of key technologies online can realize the automatic calibration of the laser system. This paper in detail describes the key technologies, such as nonlinear broadband propagation, broadband amplification and frequency conversion. Meanwhile, other auxiliary technologies are also taken into account, including paraxial ray tracing equations (PRTEs), vector electromagnetic field propagation, phase retrieval based on the iteration algorithm, grating analysis and finite-difference time-domain (FDTD) analysis of micrometer or nanometer devices, etc. During the derivation, some elementary examples of digital control of key technologies online are also provided which can verify the correction of the corresponding theories and the stability of the algorithm.