This paper describes a novel approach for monitoring the efficiency of control over ferroelectric fibrous nonwoven materials (and scaffolds based on them), which are sensitive to the electric field and irradiation using charged particle beams. The method proposed is based on the dynamic time-resolved analysis of multifractal spectra of the fiber networks and time-resolved estimation of the fractal dimensions of such networks in the external fields or under the electron beam irradiation conditions. The introduction also provides a bibliographic background for the use of fractal and multifractal approaches to the analysis of “intelligent scaffolds” and networks of electrospun polarized fibers with dynamically regulated porosity as modern structured materials for the cell growth guidance and tissue-engineering constructs. The possibility of electrodynamic analysis of the behavior of fibers and scaffolds with (multi)fractal properties in an external field using mathematical models of fractal antennas is suggested. The reference list includes 77 items and the paper contains 7 tables with various multifractal graphs.