SEMIADDITIVITY OF THE ENTROPY RAYLEIGH-RITZ OPERATOR IN THE PROBLEM OF REALIZATION OF AN INVARIANT POLYLINEAR REGULATOR OF A NON-STATIONARY HYPERBOLIC SYSTEM
Keywords:
nonlinear realization theory, non-stationary hyperbolic system, polylinear regulator, entropy Rayleigh-Ritz operator.DOI:
https://doi.org/10.17654/0974324322020Abstract
Such qualitative issues which bound up with existence of a solution for the inverse problem of systems analysis as realization solvability (sufficient conditions) of the operator functions of the polylinear regulator for a non-stationary hyperbolic system, which contains given (finite/countable/continual) nonlinear bundles of infinite-dimensional controlled dynamic processes in the capacity of admissible solutions in a separable Hilbert space, are investigated.
Received: February 23, 2022; Accepted: April 20, 2022;
References
V. A. Rusanov, L. V. Antonova and A. V. Daneev, Inverse problem of nonlinear systems analysis: a behavioral approach, Advances in Differential Equations and Control Processes 10(2) (2012), 69-88.
A. V. Lakeev, Yu. É. Linke and V. A. Rusanov, To the structure identification of a nonlinear regulator for a nonstationary hyperbolic system, Doklady Mathematics 93(3) (2016), 339-343.
A. V. Lakeev, Yu. É. Linke and V. A. Rusanov, Realization of a polylinear controller as a second-order differential system in a Hilbert space, Differ. Equ. 53(8) (2017), 1070-1081.
A. V. Daneev, V. A. Rusanov and M. V. Rusanov, From Kalman-Mesarovic realization to a normal-hyperbolic linear model, Cybernet. Systems Anal. 41(6) (2005), 909-923.
Y. Chen, A new one-parameter inhomogeneous differential realization of the spl(2, 1) super-algebra, Internat. J. Theoret. Phys.s 51(12) (2012), 3763-3768.
V. A. Rusanov, A. V. Daneev, A. V. Lakeev and Yu. É. Linke, On the differential realization theory of non-linear dynamic processes in Hilbert space, Far East J. Math. Sci. (FJMS) 97(4) (2015), 495-532.
V. A. Rusanov, A. V. Daneev, A. V. Lakeyev and V. N. Sizykh, Higher-order differential realization of polylinear-controlled dynamic processes in a Hilbert space, Advances in Differential Equations and Control Processes 19(3) (2018), 263-274.
M. Reed and B. Simon, Methods of Modern Mathematical Physics. 1. Functional Analysis, Academic Press, New York, 1972.
J. L. Massera and J. J. Schaffer, Linear Differential Equations and Function Spaces, Academic Press, New York, 1966.
V. A. Rusanov, A. V. Banshchikov, R. A. Daneev and A. V. Lakeyev, Maximum entropy principle in the differential second-order realization of a nonstationary bilinear system, Advances in Differential Equations and Control Processes 20(2) (2019), 223-248.
V. A. Rusanov and D. Yu. Sharpinskii, The theory of the structural identification of nonlinear multidimensional systems, J. Appl. Math. Mech. 74 (2010), 84-94.
V. A. Rusanov, A. V. Daneev and Yu. É. Linke, To the geometrical theory of the differential realization of dynamic processes in a Hilbert space, Cybernet. Systems Anal. 53(4) (2017), 554-564.
V. A. Rusanov, A. V. Daneev, Yu. É. Linke and P. A. Plesnyov, Existence of a bilinear delay differential realization of nonlinear neurodynamic process in the constructions of entropy Rayleigh-Ritz operator, Advances in Dynamical Systems and Applications 15(2) (2020), 199-215.
V. A. Rusanov, A. V. Lakeev and Yu. É. Linke, Solvability of differential realization of minimum dynamic order for a family of nonlinear input-output processes in Hilbert space, Differ. Equ. 51(4) (2015), 533-547.
J. L. Kelley, General Topology, New York, 1957.
L. V. Kantorovich and G. P. Akilov, Functional Analysis, Nauka, Moscow, 1977.
V. A. Rusanov, R. A. Daneev, A. V. Lakeyev and Yu. É. Linke, Differential realization of second-order bilinear system: a functional geometric approach, Advances in Differential Equations and Control Processes 19(3) (2018), 303-321.
A. V. Daneev, A. V. Lakeyev and V. A. Rusanov, Existence of a bilinear differential realization in the constructions of tensor product of Hilbert spaces, WSEAS Trans. Math. 19 (2020), 99-107.
V. A. Rusanov, A. V. Daneev, A. V. Lakeyev and Yu. É. Linke, On the theory of differential realization: criteria of continuity of the nonlinear Rayleigh-Ritz operator, International Journal of Functional Analysis, Operator Theory and Applications 12(1) (2020), 1-22.
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