Numerical solution of nonlinear inverse coefficient problems for ordinary differential equations

Айда-заде, К. Р.; Kuliev, S. Z.

doi:10.1134/s0965542511050022

Cited by 17 publications

(10 citation statements)

References 2 publications

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“…The components of the gradient of the target functional on the class of controls (8) are determined by the formulas: …”

Section: Theoremmentioning

confidence: 99%

“…, under observance of the condition (8), which satisfies the following jump condition on the interface of the zones: …”

mentioning

confidence: 99%

“…Note that the proofs of theorems 3 and 4 use the technique of obtaining necessary first order optimality conditions as applied to discontinuous systems [7]; the proofs of theorems 1 and 2 use the technique of obtaining necessary first order optimality conditions on the classes of piecewise constant and piecewise linear functions [8]. To prove theorem 5, one can use, for example, the scheme adopted in the work [9] for problems involving a non-fixed time.…”

mentioning

confidence: 99%

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Some approaches to solve feedback control problems for nonlinear dynamic systems

Айда-заде

Guliyev

2012

2012 IV International Conference "Problems of Cybernetics and Informatics" (PCI)

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Optimal feedback control problems for objects described by ordinary differential equations systems on the class of zonal control functions involving uncertain information on the values of these objects' initial conditions and parameters are investigated in the work. Zonal values of the controls are optimized in the problem considered. Formulas for the gradient of the target functional are derived. These formulas allow solving the problem numerically using efficient first order optimization methods. Results of numerical experiments carried out by the example of solution to model problems are given.

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“…The components of the gradient of the target functional on the class of controls (8) are determined by the formulas: …”

Section: Theoremmentioning

confidence: 99%

“…, under observance of the condition (8), which satisfies the following jump condition on the interface of the zones: …”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Some approaches to solve feedback control problems for nonlinear dynamic systems

Айда-заде

Guliyev

2012

2012 IV International Conference "Problems of Cybernetics and Informatics" (PCI)

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“…1512 sec.). The systems with a more general form are considered in the papers [7,8], which is determined by an unknown component in a right-hand side of the autonomous system of differential equations.…”

Section: Introductionmentioning

confidence: 99%

On algorithm of identification of nonlinear system parameters

Pogonin¹,

Onevsky²,

Pchelintsev³

2016

ams

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The problem of identification of parameters of nonlinear system of differential equations is considered in this article. It's reduced to the problem of stabilization. To solve it, we use the method which has been developed in the last decade for nonlinear systems. The original system is transformed into a form suitable for the application of the proposed method. An algorithm for identifying data is presented, a numerical experiment for searching the parameters is shown.

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“…The considered problem of determination of the function of the coeffi cient of hydraulic resistance λ(ω) has been formulated within the problem of optimum control over the system with distributed parameters, more precisely, of the problem of synthesis of control, since the running value of the identifi ed function at all x ∈ (0, l) and [ , ] i i t T T ∈ , s = 1, 2, …, N, depends on the running state of the process ω(x, t). We propose that the approach from [9] be used for numerical solution of the formulated problem. We assume that, from the a priori information on the process, we know the range of actually possible values of the velocity of motion of the liquid in the pipeline, i.e.,…”

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confidence: 99%

Numerical Method of Solution of the Coefficient-Inverse Problem for Unsteady Motion in an Oil Pipeline

Kuliev

2015

J Eng Phys Thermophy

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Consideration is given to the approach to identifi cation of the coeffi cient of hydraulic resistance of a linear portion of a main pipeline in transporting raw hydrocarbons. The problem of identifi cation is reduced to a class of fi nitedimensional-optimization problems. To solve them, the author proposes effi cient numerical methods of fi nitedimensional optimization of fi rst order. For this purpose, in the work, the author derives formulas for the components of the gradient of the target functional in the space of identifi ed parameters. The obtained values of the optimized vector can be used for construction of the identifi ed function from any class of functions with interpolation and approximation methods. Results of the conducted numerical experiments are given. Keywords: distributed system, coeffi cient of hydraulic resistance, inverse problem, identifi cation problem, conjugate problem, functional gradient.Introduction. In recent years, pipeline transport systems have become the basic and most signifi cant means of transportation of raw hydrocarbons. One recognizes two sources of energy loss in the case of liquid motion in a pipeline: loss along the pipeline length and loss in local resistances. By local resistances are meant all kinds of devices of a small length (compared to the pipe length) and various locking devices, bends, valves, etc. The loss in local resistances is caused by the enhanced mixing of the liquid, which is accompanied by vortex formation, and by large velocity gradients. The loss along the pipe length or by friction is due to the friction in the fl ow and is dependent on the pipeline length and on the coeffi cient of hydraulic resistance [1,2]. The values of resistances of the pipeline′s portions exert a substantial infl uence on the motion of oil (gas) in the pipeline. It is well known [3] that the resistance of the pipeline′s portion depends not only on such geometric dimensions of the pipe as the portion length and the pipe diameter, but also on the roughness of the interior pipe surface infl uencing the value of the coeffi cient of hydraulic resistance. In the process of long-term operation of pipelines, the coeffi cients of hydraulic resistances of portions change, namely, increase as a result of the processes of hydrate formation on the interior surface of the pipelines. These processes are the most intense when technological regimes of operation of the pipelines are violated and on installations for preparation of oil products for transporting. The development of networks of main pipelines (mains) for transportation of raw hydrocarbons is accompanied by the wide and active use of modern instrumentation and computer aids in them, and also of remote-control systems. Therefore, of practical importance is to employ mathematical methods of identifi cation of the coeffi cients of resistance for tracking of the state of potions of a pipeline network. This makes it possible to detect suspicious portions on which intense hydrate-formation processes have begun, which has a substantial ...

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Numerical solution of nonlinear inverse coefficient problems for ordinary differential equations

Cited by 17 publications

References 2 publications

Some approaches to solve feedback control problems for nonlinear dynamic systems

Some approaches to solve feedback control problems for nonlinear dynamic systems

On algorithm of identification of nonlinear system parameters

Numerical Method of Solution of the Coefficient-Inverse Problem for Unsteady Motion in an Oil Pipeline

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