Identification of the Transverse Distributed Load in the Euler-Bernoulli Beam Equation from Boundary Measurement

Saraç, Yeşim; Şener, Sıdıka Şule

doi:10.7763/ijmo.2018.v8.617

Cited by 2 publications

(2 citation statements)

References 10 publications

(11 reference statements)

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“…Linear control problems with nonlinear functional perturbations are of great interest in modern studies owing to their nontrivial mathematical structure and wide applications in diverse fields. Of special interest are nonlinearly perturbed control problems [11,25,26] with delay parameters, modeling some real situations in widely used remote control systems. The solvability and reliability of such control problems strongly depends on the topological structure [1,3,4,8,10,11,17,15,23] of the corresponding solution set, its completeness and stability.…”

Section: Introductionmentioning

confidence: 99%

Solvability, Completeness and Computational Analysis of A Perturbed Control Problem with Delays

Byszewski

Blackmore²,

Balinsky

et al. 2020

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As a first step, we provide a precise mathematical framework for the class of control problems with delays (which we refer to as the control problem) under investigation in a Banach space setting, followed by careful definitions of the key properties to be analyzed such as solvability and complete controllability. Then, we recast the control problem in a reduced form that is especially amenable to the innovative analytical approach that we employ. We then study in depth the solvability and completeness of the (reduced) nonlinearly perturbed linear control problem with delay parameters. The main tool in our approach is the use of a Borsuk-Ulam type fixed point theorem to analyze the topological structure of a suitably reduced control problem solution, with a focus on estimating the dimension of the corresponding solution set, and proving its completeness. Next, we investigate its analytical solvability under some special, mildly restrictive, conditions imposed on the linear control and nonlinear functional perturbation. Then, we describe a novel computational projection-based discretization scheme of our own devising for obtaining accurate approximate solutions of the control problem along with useful error estimates. The scheme effectively reduces the infinite-dimensional problem to a sequence of solvable finite-dimensional matrix valued tasks. Finally, we include an application of the scheme to a special degenerate case of the problem wherein the Banach-Steinhaus theorem is brought to bear in the estimation process.

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Section: Introductionmentioning

confidence: 99%

Solvability, Completeness and Computational Analysis of A Perturbed Control Problem with Delays

Byszewski

Blackmore²,

Balinsky

et al. 2020

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“…Saraç and Şener [11] have determined the transverse distributed load in Euler-Bernoulli beam problem from of admissible control. The set of admissible controls has been taken as a subspace of the space 56, 78.…”

Section: Introductionmentioning

confidence: 99%

On the Solution of a Optimal Control Problem for a Hyperbolic System

Toyoğlu¹

2018

ACM

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In this study, the problem of determining the control function that is at the right hand side of a hyperbolic system from the final observation is investigated. Using the Fourier-Galerkin method, the weak solution of this hyperbolic system is obtained. The necessary conditions for the existence and uniqueness of the optimal solution are proved. We also find the approximate solutions of the test problems in numerical examples by a MAPLE ® program. Finally, the numerical results are presented in the form of tables.

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Identification of the Transverse Distributed Load in the Euler-Bernoulli Beam Equation from Boundary Measurement

Cited by 2 publications

References 10 publications

Solvability, Completeness and Computational Analysis of A Perturbed Control Problem with Delays

Solvability, Completeness and Computational Analysis of A Perturbed Control Problem with Delays

On the Solution of a Optimal Control Problem for a Hyperbolic System

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