The process of quantum tunneling of particles in various physical systems can be controlled even by a weak and slow varying in time electromagnetic signal. During an under-barrier motion of a particle, such a signal provides a coherent assistance of tunneling. This takes place by the multiquanta absorption resulting in a strong enhancement of the tunneling probability. For tunneling, the semiclassical approach based on trajectories in the complex time is developed. Enhancement of tunneling occurs when a singularity of the signal coincides in position at the complex time plane.
