Controlling the spatial structure of vector beams synthesized by a fiber laser array

•This paper presents a mathematical model and experimental implementation of a new method for controlling the spatial intensity distribution of a synthesized beam with nonuniformly distributed polarization.•The method is based on phase control of elements of an array of coherent emitters with the given distribution of directions of linear polarization.•The phase control is based on the well-known SPGD optimization algorithm in combination with the use of a phase corrector in the feedback loop.•The results of controlling the spatial structure of the beam are presented for phase correctors of two types.