To Existence of a Nonstationary Quasi-Linear Vector Field Realizing the Expansion of a Control Trajectory Bundle in Hilbert Space

Abstract

 The study of algebraic extension of a countable family of controlled non-linear dynamic processes "inputoutput" having differential realization in the class of ordinary quasi-linear differential equations (with software-positional control and without) in a separable Hilbert space was conducted. This problem as a starting point for the development of the general theory of vector fields, simultaneously creating a reputation for it as a useful tool in precision mathematical modeling of complex dynamic systems.

An Inverse Problems for Nonlinear Evolution Equations: Criteria of Existence of an Invariant Polylinear Controller for a Second-Order Differential System in a Hilbert Space

“…Inverse problems of evolution equations (IPEE), as a section of the differential realization of dynamical systems, currently represent a fairly extensive area of research [110]. In this context, the proposed work continues research [2,10], while understanding the nature of hyperbolic systems (in the technical sense) helps to clarify and motivate the entire discussion. Its main goal is to study the problem of existence of coefficient operator-functions of an invariant polylinear controller (IPL-controller) of a non-stationary differential system (D-system) 1 of the second order; however, its results can be extended to stationary D-systems [11].…”