Controllability of vibrations of a net of coupled objects with distributed and lumped parameters

Егоров, А. И.; Znamenskaya, L. N.

doi:10.1134/s0965542509050054

Cited by 5 publications

(5 citation statements)

References 2 publications

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“…It should be noted that the expediency of considering optimal control problems for systems containing links with distributed parameters is associated with the fact that control of an object with distributed parameters in real systems is carried out by control devices with lumped parameters. A cycle of papers [3][4][5] is devoted to the theoretical study of this type of optimal control problems.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…In [3,4], the problem of damping oscillations of a system described by a combination of a wave equation and an ordinary differential equation of the second order is considered, under the assumption that the control function and the object with lumped parameters act, respectively, on the left and right ends of the object with distributed parameters. The functions of the system states are related through the boundary conditions for the wave equation.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…The problem of oscillation control and the results are formulated, which determines the general solution of the boundary value problem. In [4], which is a continuation of [3], a solution of the boundary value problem was constructed and the control problem was solved. Further, using the method of straight lines, a finite-dimensional approximation of the boundary value problem is constructed and a criterion for the controllability of the system is found.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…In [5], the problem of damping oscillations of a network consisting of m objects with distributed parameters is solved, in which a controlled object with lumped parameters acts through the boundary conditions at the point of connection of objects. The solution of the boundary value problem is constructed and the control problem is solved.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of one class of optimal control problems for distributed-parameter systems

Mamtiyev

Aliyeva

Rzayeva

2021

EEJET

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In the paper, the method of straight lines approximately solves one class of optimal control problems for systems, the behavior of which is described by a nonlinear equation of parabolic type and a set of ordinary differential equations. Control is carried out using distributed and lumped parameters. Distributed control is included in the partial differential equation, and lumped controls are contained both in the boundary conditions and in the right-hand side of the ordinary differential equation. The convergence of the solutions of the approximating boundary value problem to the solution of the original one is proved when the step of the grid of straight lines tends to zero, and on the basis of this fact, the convergence of the approximate solution of the approximating optimal problem with respect to the functional is established. A constructive scheme for constructing an optimal control by a minimizing sequence of controls is proposed. The control of the process in the approximate solution of a class of optimization problems is carried out on the basis of the Pontryagin maximum principle using the method of straight lines. For the numerical solution of the problem, a gradient projection scheme with a special choice of step is used, this gives a converging sequence in the control space. The numerical solution of one variational problem of the mentioned type related to a one-dimensional heat conduction equation with boundary conditions of the second kind is presented. An inequality-type constraint is imposed on the control function entering the right-hand side of the ordinary differential equation. The numerical results obtained on the basis of the compiled computer program are presented in the form of tables and figures. The described numerical method gives a sufficiently accurate solution in a short time and does not show a tendency to «dispersion». With an increase in the number of iterations, the value of the functional monotonically tends to zero

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of one class of optimal control problems for distributed-parameter systems

Mamtiyev

Aliyeva

Rzayeva

2021

EEJET

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“…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%

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

Егоров

Znamenskaya

2012

Comput. Math. and Math. Phys.

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Controllability of vibrations of a net of coupled objects with distributed and lumped parameters

Cited by 5 publications

References 2 publications

Analysis of one class of optimal control problems for distributed-parameter systems

Analysis of one class of optimal control problems for distributed-parameter systems

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

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

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