Boundary observability of elastic vibrations in a system of sequentially connected strings

Егоров, А. И.; Znamenskaya, L. N.

doi:10.1134/s0965542512070056

Cited by 1 publication

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“…For the efficient numerical solution of this problem, two methods were utilized: the gradient projection method, based on obtaining formulas (19) for the first variation of the functional (7), and the method of successive approximations due to the linearity of the boundary value problems describing the oscillatory processes (1)- (5). The proposed algorithm for the numerical solution of the problem was implemented in software code, enabling practical results to be obtained.…”

Section: Discussion Of the Results Of Solving The Problem Of Optimal ...mentioning

confidence: 99%

“…The main drawback of the work, which should be paid attention to, is the significant computational difficulties in constructing and solving boundary value problems and the control variable presented in [5][6][7]. Nevertheless, these formulas have important theoretical significance in the study of the control of oscillation processes in coupled systems, consisting of objects with distributed and lumped parameters.…”

Section: Discussion Of the Results Of Solving The Problem Of Optimal ...mentioning

confidence: 99%

“…The optimization of oscillatory processes holds significant relevance across various fields, encompassing endeavors such as stabilizing ship motions, managing crane booms, and controlling gas flows in extensive pipelines or power lines [1][2][3][4]. Notably, recent studies [5][6][7][8] have broached the challenges of damping oscillations within systems described by a combination of wave equations and second-order ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…

Specifically, [5] addresses scenarios where a fixed boundary on the left and an object with lumped parameters on the right impact the distributed system. Conversely, [6] tackles cases where control functions and objects with lumped parameters influence the system's ends, interlinked through the boundary conditions of the wave equation.

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confidence: 99%

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Finding and implementing the numerical solution of an optimal control problem for oscillations in a coupled objects system

Mamtiyev,

Rzayeva

2024

EEJET

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In the modern world, where efficiency, stability, and precision play a crucial role, the development and application of optimal control strategies in oscillatory systems hold significant importance. The issues related to the numerical solution of control problems associated with damping oscillatory systems consisting of two objects are considered. To numerically solve the discussed problem, the gradient projection method, based on the formula for the first variation of the functional, and the method of successive approximations, associated with the linearity of boundary problems describing oscillatory processes, are applied. The oscillations of one object are described by a wave equation with first-order boundary conditions, while a second-order ordinary differential equation models the oscillations of the other object. Furthermore, the original and the adjoint boundary value problems are solved using direct methods at each iteration step. An algorithm for the numerical solution of the problem is proposed, and based on this algorithm, a software code for implementation is developed. The numerical results obtained in the study demonstrate that there is convergence in terms of functionality, and the approximately optimal controls found in this process are minimizing sequences in the control space. The mechanism of controlling and regulating the operation of the system according to its input constraints is provided by observed feedback, allowing systems with limited excitation to maintain stability and optimal functioning in conditions of changing external or internal circumstances. The obtained results can also be used to forecast the system's behavior in the future, resource planning, prevention of emergencies, or optimization of production processes

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Section: Discussion Of the Results Of Solving The Problem Of Optimal ...mentioning

confidence: 99%

Section: Discussion Of the Results Of Solving The Problem Of Optimal ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

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Finding and implementing the numerical solution of an optimal control problem for oscillations in a coupled objects system

Mamtiyev,

Rzayeva

2024

EEJET

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Boundary observability of elastic vibrations in a system of sequentially connected strings

Cited by 1 publication

References 1 publication

Finding and implementing the numerical solution of an optimal control problem for oscillations in a coupled objects system

Finding and implementing the numerical solution of an optimal control problem for oscillations in a coupled objects system

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