Averaging of aperiodic problems of control over fracture surfaces

Плотников, В. А.; Zverkova, Tatyana; Slobodyanyuk, O. E.

doi:10.1007/bf01066097

Cited by 2 publications

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“…In this review we have not considered the V.A. Plotnikov's results devoted to the averaging of the differential equations with discontinuous right-hand side in case of the sliding mode [5,26,27], to the application of the averaging method and differential inclusions to the research of control problems [1,2,4,7,28,29,30,31,32,33], to averaging of discrete inclusions [34], to questions of asymptotical researches of singularly perturbed differential inclusions and to the generalization of the A.N. Tikhonov theorem on differential inclusions [4,35,36,37].…”

Section: (T) Of the Inclusion (125) -(127) There Exists A Solution Y(mentioning

confidence: 99%

Overview of V.A. Plotnikov’s research on averaging of differential inclusions

Klymchuk

Plotnikov

Skripnik

2012

Physica D: Nonlinear Phenomena

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In this review we will first look in detail at V.A. Plotnikov's results on the substantiation of full and partial schemes of averaging for differential inclusions in the standard form on final and infinite interval. Then we will consider the algorithms where there is no average, but there is a possibility to find its estimation from below and from above. Such approach is also used when the detection of an average is approximate. This situation is especially typical at consideration of differential inclusions with fast and slow variables. In the last part we will give the results concerning the substantiation of the full and partial averaging method for impulsive differential inclusions on final and infinite intervals.

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Section: (T) Of the Inclusion (125) -(127) There Exists A Solution Y(mentioning

confidence: 99%

Overview of V.A. Plotnikov’s research on averaging of differential inclusions

Klymchuk

Plotnikov

Skripnik

2012

Physica D: Nonlinear Phenomena

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“…Different problems described by differential equations with discontinuous r.h.s. were studied in [70,78,59,101,102,16].…”

Section: Differential Inclusions With a Discontinuous Rhsmentioning

confidence: 99%

Stability and Optimality of Solutions to Differential Inclusions via Averaging Method

Gama

Smirnov

2013

Set-Valued Var. Anal

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The averaging method is one of the most used tools to study dynamical systems. With the development of the theory of differential inclusions, a respective generalization of the averaging method followed the steps outlined in the theory of differential equations. Presently, it has been successfully applied to a wide range of problems involving differential inclusions, simplifying the study of the systems under consideration. In this work, the main development trends and methods in the application of the averaging method to the study of stability and optimality of solutions to differential inclusions are surveyed. A detailed list of references is given and some examples of applications are presented.

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Averaging of aperiodic problems of control over fracture surfaces

Cited by 2 publications

References 0 publications

Overview of V.A. Plotnikov’s research on averaging of differential inclusions

Overview of V.A. Plotnikov’s research on averaging of differential inclusions

Stability and Optimality of Solutions to Differential Inclusions via Averaging Method

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