Exact null controllability of abstract differential equations by finite-dimensional control and strongly minimal families of exponentials

Shklyar, B.

doi:10.7153/dea-03-10

Cited by 8 publications

(12 citation statements)

References 19 publications

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“…One way to analyze the controllability problem is a technique based on the problem of moments and Riesz basis. In [18,19], this technique has been implemented for systems of neutral type in case of reachability and exact zero-controllability problems. A more complete history of the development of each of these methods can be traced back through the corresponding references [8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…In the present work, which is a continuation of [21][22][23], we propose a control method for systems of neutral type with many commensurable delays in both state and control in case when both of these complete controllability conditions are violated. Note that the said spectral condition is also necessary for feasibility and other problems [14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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Complete controllability and controllability for linear autonomous systems of neutral type

Khartovskii

Pavlovskaya

2013

Autom Remote Control

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complete controllability and controllability for linear autonomous systems of neutral type

Khartovskii

Pavlovskaya

2013

Autom Remote Control

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“…The existence of a basis of the state space consisting of eigenvectors (or generalized eigenvectors) essentially simplifies the expression of the moment problem (see [18] and [22]). In our case, the existence of a basis of eigenvectors is determined by the form of the matrix A −1 of the neutral term of the system (1.1), and, in general, such basis does not exist (see [15,16]).…”

Section: Introductionmentioning

confidence: 99%

On Exact Controllability of Time-Delay Systems of Neutral Type

Rabah¹,

Sklyar

Barkhayev

2016

Ukr Math J

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The paper is devoted to the problem of exact controllability for a wide class of neutral and mixed time-delay systems. We consider an equivalent operator model in Hilbert space and formulate steering conditions of controllable states as a vector moment problem. The existence of a basis of eigenvectors of the system operator enables the form of the moment problem to be substantially simplified. A change in control by a feedback law modifies the system structure to guarantee the existence of a basis of eigenvectors of the corresponding operator. We prove a criterion of exact controllability and ascertain the precise critical time of controllability. Анотацiя Робота присвячена вирiшенню задачi точної керованостi для досить широкого класу систем з запiзненням нейтрального та змiшаного типiв. Розглядаючи еквiвалентну операторну модель в гiльбертовому просторi, ми формулюємо умови керованостi у виглядi деякої векторної проблеми моментiв. Вид даної проблеми моментiв iстотно спрощується при наявностi базису простору з власних векторiв оператора системи з запiзненням. Замiна керування дозволяє перетворити структуру системи, i гарантувати iснування базису з власних векторiв вiдповiдного оператора. Ми доводимо критерiй точної керованостi i встановлюємо точний час керування. Аннотация Данная работа посвящена решению задачи точной управляемости для достаточно широкого класса систем с запаздыванием нейтрального и смешанного типов. Рассматривая эквивалентную операторную модель в гильбертовом пространстве, мы формулируем условия управляемости в виде некоторой векторной проблемы моментов. Вид данной проблемы моментов существенно упрощается при наличии базиса пространства из собственных векторов оператора системы с запаздыванием. Замена управления позволяет преобразовать структуру системы, и гарантировать существование базиса из собственных векторов соответствующего оператора. Мы доказываем критерий точной управляемости и устанавливаем точное время управления.

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“…We introduce extra two definitions of -controllability employed actively in considering systems (10) (see, for instance, [8,10]). …”

Section: Relations Between Various Notions Of -Controllabilitymentioning

confidence: 99%

“…Sholokhovich [4], A.B. Kurzhanski [5], R. Triggiani [6], B. Shklyar [7,8] and many other (see also surveys [9,10,11] and works [12,13]). …”

Section: Introductionmentioning

confidence: 99%

On control of degenerate distributed systems

Плеханова¹,

Федоров²

2014

Ufimskii Matematicheskii Zhurnal

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Abstract. We study the controllability of linear distributed control systems described by differential equations in Banach spaces with a degenerate operator at the derivative. A homogeneous part of equations has a degenerate strongly continuous resolving semigroup. For such system with, generally speaking, a time-dependent bounded operator at the control function we find the criteria of -controllability in time and of -controllability in a free time in terms of the operators involved in the equation. General results are used for studying of -controllability of the considered systems with a finite-dimensional input. The obtained conditions are demonstrated by examples of control systems described by partial differential equations and systems of equations unsolved with respect to the time derivative.

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Exact null controllability of abstract differential equations by finite-dimensional control and strongly minimal families of exponentials

Cited by 8 publications

References 19 publications

Complete controllability and controllability for linear autonomous systems of neutral type

Complete controllability and controllability for linear autonomous systems of neutral type

On Exact Controllability of Time-Delay Systems of Neutral Type

On control of degenerate distributed systems

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