The work is carried out as part of the program to construct a new functional (so-called wave) model of symmetric operators. It is shown that an abstract evolutionary dynamic system of the first order (with respect to time) with boundary control, which is determined by a symmetric operator L₀ : [InlineMediaObject not available: see fulltext.] → [InlineMediaObject not available: see fulltext.], is controllable if and only if L₀ has no maximal symmetric parts in [InlineMediaObject not available: see fulltext.].