DISTRIBUTED CONTROL FOR 2 x 2 COUPLED INFINITE ORDER HYPERBOLIC SYSTEMS

Qamlo, A. H.; Bedaiwi, G. M.

doi:10.17654/de018040201

Cited by 3 publications

(7 citation statements)

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“…The Sobolev spaces of infinite order operators, which are used in this study, have already been presented in Reference [13]. We list them briefly below:…”

Section: Necessary Spacesmentioning

confidence: 99%

“…Majority of the research in this field has focused on discussing the optimal control problem by using several operator types (such as elliptic, parabolic, or hyperbolic operators) [2]- [11], and by varying the nature of control (such as distributed control [6] [11] [12] [13] and boundary control [3] [5] [8]).…”

Section: Introductionmentioning

confidence: 99%

“…Based on the theories proposed by Lions [1] and Dubinskii [22] [23] [24], the distributed control problem with Dirichlet conditions for 2 × 2 non-cooperative hyperbolic systems involving infinite order operators was discussed in a previous study [13]; in this study, we extend this problem to cooperative hyperbolic sys-tems of the boundary type with Neumann conditions for different observation functions.…”

Section: Introductionmentioning

confidence: 99%

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Boundary Control Problems for 2 × 2 Cooperative Hyperbolic Systems with Infinite Order Operators

Qamlo¹

2021

OJOp

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“…The Sobolev spaces of infinite order operators, which are used in this study, have already been presented in Reference [13]. We list them briefly below:…”

Section: Necessary Spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Boundary Control Problems for 2 × 2 Cooperative Hyperbolic Systems with Infinite Order Operators

Qamlo¹

2021

OJOp

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“…The Sobolev spaces of infinite order operators, which are used in this study, have already been presented in Reference [17].…”

Section: Necessary Spaces: [18] [19] [20]mentioning

confidence: 99%

“…Based on the theories proposed by Lions [1] and Dubinskii [18] [19] [20], the distributed control problem with Dirichlet conditions for 2 × 2 non-cooperative hyperbolic systems involving infinite order operators was discussed in a previous study [17]; in this study, we extend this problem to n × n cooperative hyperbolic systems.…”

Section: Introductionmentioning

confidence: 99%

Distributed Control for <i>n</i> × <i>n</i> Cooperative Systems Governed by Hyperbolic Operator of Infinite Order

Qamlo¹

2020

APM

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In this study, a distributed optimal control problem for n × n cooperative hyperbolic systems with infinite order operators and Dirichlet conditions are considered. The existence and uniqueness of the state of these systems are proved. The necessary and sufficient conditions for optimality of distributed control with constraints are found, and the set of equations and inequalities that defining the optimal control of these systems is also obtained. Finally, some examples for the control problem without constraints are given.

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Boundary Control for Cooperative Elliptic Systems under Conjugation Conditions

Serag¹,

Abdelrhman²,

Alsaban³

2021

APM

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The existence and uniqueness of the state for 2 × 2 Dirichlet cooperative elliptic systems under conjugation conditions are proved using Lax-Milgram lemma, then the boundary control for these systems is discussed. The set of equations and inequalities that characterizes this boundary control is found by theory of Lions, Sergienko and Deineka. The problem for cooperative Neumann elliptic systems under conjugation conditions is also considered.Finally, the problem for n × n cooperative elliptic systems under conjugation conditions is established.

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DISTRIBUTED CONTROL FOR 2 x 2 COUPLED INFINITE ORDER HYPERBOLIC SYSTEMS

Cited by 3 publications

References 0 publications

Boundary Control Problems for 2 × 2 Cooperative Hyperbolic Systems with Infinite Order Operators

Boundary Control Problems for 2 × 2 Cooperative Hyperbolic Systems with Infinite Order Operators

Distributed Control for <i>n</i> × <i>n</i> Cooperative Systems Governed by Hyperbolic Operator of Infinite Order

Boundary Control for Cooperative Elliptic Systems under Conjugation Conditions

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DISTRIBUTED CONTROL FOR 2 x 2 COUPLED INFINITE ORDER HYPERBOLIC SYSTEMS

Cited by 3 publications

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Boundary Control Problems for 2 &#215; 2 Cooperative Hyperbolic Systems with Infinite Order Operators

Boundary Control Problems for 2 &#215; 2 Cooperative Hyperbolic Systems with Infinite Order Operators

Distributed Control for &lt;i&gt;n&lt;/i&gt; &#215; &lt;i&gt;n&lt;/i&gt; Cooperative Systems Governed by Hyperbolic Operator of Infinite Order

Boundary Control for Cooperative Elliptic Systems under Conjugation Conditions

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Boundary Control Problems for 2 × 2 Cooperative Hyperbolic Systems with Infinite Order Operators

Boundary Control Problems for 2 × 2 Cooperative Hyperbolic Systems with Infinite Order Operators

Distributed Control for <i>n</i> × <i>n</i> Cooperative Systems Governed by Hyperbolic Operator of Infinite Order