On realization of multiple-linear regulator of non-stationary hyperbolic system

The article studies some qualitative issues of the existing a solution to inverse problem of nonlinear infinite-dimensional system analysis, regarding the solvability of the operator realization of invariant multiple-linear regulator of non-stationary hyperbolic system. The studied statement for precision mathematical modeling considers the case, when for two different beams (finite, countable, or even continuous) of nonlinear controlled dynamic processes of the “trajectory, program control” type, induced in a real separable Hilbert space by some given non-stationary hyperbolic system, but with different multiple-linear regulators, we obtain sufficient conditions for solvability of the problem of realizing operator functions of a general (invariant) multiple-linear regulator, in which presence in equation structure of a given hyperbolic system the union of these dynamic beams represent a fixed family of its admissible solutions. The study was carried out in the light of modern ideas about the geometry of infinite-dimensional vector fields and based on a qualitative study of the semi-additivity of non-linear Rayleigh-Ritz functional operator.