Approximate Controllability of Strongly Degenerate Fractional Order System of Distributed Control

Fedorov, Vladimir E.; Gordievskikh, Dmitriy M.

doi:10.1016/j.ifacol.2018.11.503

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…. , y m−1 ) in (17) and with a control function u. Denoted by y(T; y; u), the value at the time T of the solution for the subsystem, described by (19), (20). And by x 0 (T; u) denotes the value at t = T of function (21).…”

Section: Approximate Controllability Of Subsystemsmentioning

confidence: 99%

“…For various classes of degenerate (ker L = {0}) systems (3) of the order α = 1 the controllability and the approximate controllability were researched in References [10][11][12][13][14]. In References [15][16][17] the approximate controllability issues are studied for system (3) of fractional order α under the condition of (L, p)-boundedness of the operator M, it is a more restrictive condition on the pair of operators L, M than in this work.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case

et al. 2019

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We consider a class of linear inhomogeneous equations in a Banach space not solvable with respect to the fractional Caputo derivative. Such equations are called degenerate. We study the case of the existence of a resolving operators family for the respective homogeneous equation, which is an analytic in a sector. The existence of a unique solution of the Cauchy problem and of the Showalter-Sidorov problem to the inhomogeneous degenerate equation is proved. We also derive the form of the solution. The approximate controllability of infinite-dimensional control systems, described by the equations of the considered class, is researched. An approximate controllability criterion for the degenerate fractional order control system is obtained. The criterion is illustrated by the application to a system, which is described by an initial-boundary value problem for a partial differential equation, not solvable with respect to the time-fractional derivative. As a corollary of general results, an approximate controllability criterion is obtained for the degenerate fractional order control system with a finite-dimensional input. Mathematics 2019, 7, 735 2 of 15 homogeneous ( f ≡ 0) Equation (1). The existence of a unique solution of the Cauchy problem and of the Showalter-Sidorov problem

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Section: Approximate Controllability Of Subsystemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case

et al. 2019

Self Cite

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On approximate controllability of a class of degenerate fractional order distributed systems

Fedorov

Gordievskikh

Filin

2021

J. Phys.: Conf. Ser.

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The approximate controllability issues for a class of control systems, whose dynamics is described by an equation in a Banach space with a linear degenerate operator at the Riemann — Liouville fractional derivative, is investigated. Under the condition of p-boundedness of the pair of operators in the equation the control system is reduced to subsystems on two mutually complement subspaces. It was shown that the approximate controllability of the whole system is equivalent to the approximate controllability of the two subsystems. Criteria of the approximate controllability for the system and two subsystems are obtained. Analogous results are got on the approximate controllability for free time and for systems of the same form with a finite-dimensional input. The obtained criteria were applied to the investigation of the approximate controllability for a distributed system with polynomials of a differential with respect to the spatial variables self-adjoint elliptic operator and for a system of the Scott-Blair — Oskolkov type.

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Approximate Controllability of Strongly Degenerate Fractional Order System of Distributed Control

Cited by 2 publications

References 15 publications

Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case

Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case

On approximate controllability of a class of degenerate fractional order distributed systems

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