We investigate the solvability of the problem of realization of operator-functions of invariant linear regulator (IL-regulator) of a second order nonstationary differential system (D-system), which allows for a finite bundle of integral curves of “trajectory, control” type, induced in this D-system by different bilinear regulators, to reduce this bundle to a subfamily of admissible solutions of this D-system through action of IL-regulator. The problem under consideration belongs to the type of nonstationary coefficient-operator inverse problems for evolution equations (including the hyperbolic) in separable Hilbert space. The problem is solved on the basis of a qualitative study of the continuity and semiadditivity properties of the nonlinear Rayleigh-Ritz functional operator. The obtained results have applications in the theory of nonlinear infinite-dimensional adaptive dynamical systems for a class of bilinear differential models of higher orders.

inverse problems of evolution equations, second-order unsteady differential system, invariant linear regulator, metric properties of the Rayleigh-Ritz operator.

Received: February 1, 2023; Accepted: March 20, 2023; Published: May 27, 2023

How to cite this article: A. V. Lakeyev, V. A. Rusanov, A. V. Daneev and Yu. D. Aksenov, On realization of the superposition principle for a finite bundle of integral curves of a second-order bilinear differential system, Advances in Differential Equations and Control Processes 30(2) (2023), 169-197. http://dx.doi.org/10.17654/0974324323011

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