An exact null controllability of stochastic singular systems

Ge, Zhaoqiang; Ge, Xiao

doi:10.1007/s11432-019-9902-y

Cited by 12 publications

(6 citation statements)

References 9 publications

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“…However, in reality, there are many unpredicted parameters and different types of uncertainty that have not been implemented in the mathematical modelling process of this system. Nonetheless, according to [32]- [33], we can consider a stochastic version of the implicit system (19) with the standard Wiener process ( ) used to model the uncertainties of the form:…”

Section: An Illustrative Examplementioning

confidence: 99%

Stochastic GE-evolution operator method for controllability of time varying stochastic implicit systems in Banach spaces

2024

Preprint

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This paper discusses exact and approximate controllability and exact and approximate observability of time varying stochastic implicit systems by GE-evolution operator method in Banach spaces. Firstly, we discuss existence and uniqueness of the mild solution to time varying stochastic implicit systems by stochastic GE-evolution operator in Banach space. Secondly, we discuss conditions for exact and approximate controllability and exact and approximate observability of the systems considered in terms of stochastic GE-evolution operator and the dual principle. Finally, an illustrative example is given.

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Section: An Illustrative Examplementioning

confidence: 99%

Stochastic GE-evolution operator method for controllability of time varying stochastic implicit systems in Banach spaces

2024

Preprint

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“…Now, we consider the initial value problem (34). In the following, assume that the solution to (33) is the strong solution in the ordinary sense and (34) admits the stochastic Laplace transform (see [68]). Applying the stochastic Laplace transform to (34), we have…”

Section: Controllability Of Finite Dimensional Stochastic Singular Li...mentioning

confidence: 99%

Review of the Latest Progress in Controllability of Stochastic Linear Systems and Stochastic GE-Evolution Operator

2021

Mathematics

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According to the spatial dimension, equation type, and time sequence, the latest progress in controllability of stochastic linear systems and some unsolved problems are introduced. Firstly, the exact controllability of stochastic linear systems in finite dimensional spaces is discussed. Secondly, the exact, exact null, approximate, approximate null, and partial approximate controllability of stochastic linear systems in infinite dimensional spaces are considered. Thirdly, the exact, exact null and impulse controllability of stochastic singular linear systems in finite dimensional spaces are investigated. Fourthly, the exact and approximate controllability of stochastic singular linear systems in infinite dimensional spaces are studied. At last, the controllability and observability for a type of time-varying stochastic singular linear systems are studied by using stochastic GE-evolution operator in the sense of mild solution in Banach spaces, some necessary and sufficient conditions are obtained, the dual principle is proved to be true, an example is given to illustrate the validity of the theoretical results obtained in this part, and a problem to be solved is introduced. The main purpose of this paper is to facilitate readers to fully understand the latest research results concerning the controllability of stochastic linear systems and the problems that need to be further studied, and attract more scholars to engage in this research.

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“…If for some concrete engineering practice, the following data are taken in (17): Therefore, kerO T 0 = {0}, i.e., System ( 18) is approximately observable by Corollary 4.5.…”

Section: Illustrative Examplementioning

confidence: 99%

“…Stochastic singular systems are inherent in many application fields, among them we mention input-output economics, temperature distribution in a composite heat conductor, the problem of protein folding, voltage distribution in electromagnetically coupled superconductive circuits, the modelling of multi-body mechanisms, signal propagation in a system of electrical cables, etc (e.g., [1][2][3][4][5][6][7]). Many results have been obtained for the study of stochastic singular systems in finite dimensional case (e.g., [6][7][8][9][10][11][12][13][14][15][16][17]), but there are few results in infinite dimensional case (see references [1][2][3][4][5]). The main reason for the difficulty lies in the change of dimemsion and the unboundedness of the state operator.…”

Section: Introductionmentioning

confidence: 99%

Controllability and Observability of Stochastic Singular Systems in Banach Spaces

2021

J Syst Sci Complex

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Exact (approximate) controllability and exact (approximate) observability of stochastic singular systems in Banach spaces are discussed. Firstly, the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces. Secondly, the necessary and sufficient conditions for the exact (approximate) controllability and exact (approximate) observability of the systems considered are derived in terms of GE-semigroup, and the dual principle is given. Thirdly, an illustrative example is given.

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An exact null controllability of stochastic singular systems

Cited by 12 publications

References 9 publications

Stochastic GE-evolution operator method for controllability of time varying stochastic implicit systems in Banach spaces

Stochastic GE-evolution operator method for controllability of time varying stochastic implicit systems in Banach spaces

Review of the Latest Progress in Controllability of Stochastic Linear Systems and Stochastic GE-Evolution Operator

Controllability and Observability of Stochastic Singular Systems in Banach Spaces

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