Absolute Stability of a Program Manifold of Non-Autonomous Basic Control Systems

Zhumatov, S. S.

doi:10.32014/2018.2518-1726.15

Cited by 3 publications

(5 citation statements)

References 8 publications

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“…The fulfillment of the indicated conditions means that the conditions of the following existence and uniqueness theorem are satisfied for system (4). .…”

Section: Poisson Stability Of the Difference Dynamic Systemsmentioning

confidence: 99%

“…Using this differential operator Poisson stability of solutions of the ordinary differential equations is studied. In [4] the problem of stability of a program manifold with respect to the given vector-function of non-autonomous basic control systems with stationary nonlinearity is investigated.…”

Section: Introductionmentioning

confidence: 99%

“…From a physical point of view, the record , , is more appropriate. In this case, obviously, the concept of solution of the difference-dynamic system (4) and the concept of the function , corresponding to it, are equivalent. Definition 2.…”

mentioning

confidence: 99%

“…Then we say that , , is a motion of a non-autonomous difference-dynamic system [7] if the pair , ∈ is fixed. From the above definition it can be seen that the concept of motion is broader than the concept of the solution of difference-dynamic system (4). Thus, in particular, the mapping , , does not have to be differentiable with respect to , not to mention , .…”

mentioning

confidence: 99%

See 3 more Smart Citations

On Lagrange Stability and Poisson Stability of the Differential-Dynamic Systems

Bapaev¹,

Vassilina²

2019

THE NATIONAL ACADEMY OFSCIENCES OF THE REPUBLIC OF KAZAKHSTAN

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Б а с р е д а к т о р ы ф.-м.ғ.д., проф., ҚР ҰҒА академигі Ғ.М. Мұтанов Р е д а к ц и я а л қ а с ы: Жұмаділдаев А.С. проф., академик (Қазақстан) Кальменов Т.Ш. проф., академик (Қазақстан) Жантаев Ж.Ш. проф., корр.-мүшесі (Қазақстан) Өмірбаев У.У. проф. корр.-мүшесі (Қазақстан) Жүсіпов М.А. проф. (Қазақстан) Жұмабаев Д.С. проф. (Қазақстан) Асанова А.Т. проф. (Қазақстан) Бошкаев К.А. PhD докторы (Қазақстан) Сұраған Д. корр.-мүшесі (Қазақстан) Quevedo Hernando проф. (Мексика), Джунушалиев В.Д. проф. (Қырғыстан) Вишневский И.Н. проф., академик (Украина) Ковалев А.М. проф., академик (Украина) Михалевич А.А. проф., академик (Белорус) Пашаев А. проф., академик (Əзірбайжан) Такибаев Н.Ж. проф., академик (Қазақстан), бас ред. орынбасары Тигиняну И. проф., академик (Молдова) «ҚР ҰҒА Хабарлары. Физика-математикалық сериясы».

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“…The fulfillment of the indicated conditions means that the conditions of the following existence and uniqueness theorem are satisfied for system (4). .…”

Section: Poisson Stability Of the Difference Dynamic Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

On Lagrange Stability and Poisson Stability of the Differential-Dynamic Systems

Bapaev¹,

Vassilina²

2019

THE NATIONAL ACADEMY OFSCIENCES OF THE REPUBLIC OF KAZAKHSTAN

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“…In 7, a set of ordinary differential equations is constructed that have a given integral curve. The inverse problems of constructing automatic control systems for program motion are studied in [8][9][10][11]. It should be noted that one of the general methods for solving inverse problems of dynamics in the class of ordinary differential equations, namely, the quasi-inversion method was proposed in [3].…”

mentioning

confidence: 99%

On Inverse Stochastic Reconstruction Problem

Tleubergenov¹,

Vassilina²,

Sarypbek³

2021

News of NAS RK. SPh-M

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In this paper, general reconstruction problem in the class of second-order stochastic differential equations of the Ito type is considered for given properties of motion, when the control is included in the drift coefficient. And the form of control parameters is determined by the quasi-inversion method, which provides necessary and sufficient conditions for existence of a given integral manifold. Further, the solution of the Meshchersky’s stochastic problem is given, which is one of the inverse problems of dynamics and, according to the well-known Galiullin’s classification, refers to the restoration problem. It is assumed that random perturbations belong to the class of processes with independent increments. To solve the posed problem an equation of perturbed motion is drawn up by the Ito rule of stochastic differentiation. And, further, the Erugin method in combination with the quasi-inversion method is used to construct: 1) a set of control vector functions and 2) a set of diffusion matrices that provide necessary and sufficient conditions for a given second-order differential equation of Ito type to have a given integral manifold. The linear case of a stochastic problem with drift control is considered separately. In the linear setting, in contrast to the nonlinear formulation, the conditions of solvability in the presence of random perturbations from the class of processes with independent increments coincide with the conditions of solvability in a similar linear case in the presence of random perturbations from the class of independent Wiener processes. Also considered is the scalar case of the recovery problem with drift controls.

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Stability of the program manifold of automatic indirect control systems taking into account the external load

Zhumatov

Mynbayeva

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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The problems of stability system that arises in the construction of different automatic systems of indirect control are considered. It is known that a given program is not always exactly performed, since there are always initial, constantly acting perturbations. Therefore, it is also reasonable to require the stability of the program manifold itself with respect to some function. In the first part, the stability being investigated of automatic indirect control systems with rigid and tachometric feedback. Necessary and sufficient conditions for the absolute stability of a program manifold are established separately. In the second part, the automatic systems of indirect control taking into account the external load are considered. The equations of the hydraulic actuator, taking into account the action of an external load, are presented in a convenient form for research. Then it reduces to studying the stability of the system of equations with respect to a given program manifold. By constructing LyapunovВ’s functions for the system in canonical form, sufficient conditions are obtained for the absolute stability of the program manifold. The results obtained can be used in the construction of stable automatic indirect control systems.

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Absolute Stability of a Program Manifold of Non-Autonomous Basic Control Systems

Cited by 3 publications

References 8 publications

On Lagrange Stability and Poisson Stability of the Differential-Dynamic Systems

On Lagrange Stability and Poisson Stability of the Differential-Dynamic Systems

On Inverse Stochastic Reconstruction Problem

Stability of the program manifold of automatic indirect control systems taking into account the external load

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