Controllability and observability of stochastic implicit systems and stochastic GE-evolution operator

Ge, Zhaoqiang

doi:10.3934/naco.2021009

Cited by 5 publications

(3 citation statements)

References 26 publications

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“…The necessary and sufficient condition for the stochastic singular linear system (58) to be approximately controllable on [0, b] is ran(C b 0 ) = L 2 (Ω, F b , P, D 1 ). The practical example can be found in [81] if there is a need.…”

Section: Controllability Of System (58)mentioning

confidence: 99%

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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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Section: Controllability Of System (58)mentioning

confidence: 99%

“…[81]). Stochastic singular system(58) is exactly controllable on [0, b] if, and only if, ran(C b 0 ) = L 2 (Ω, F b , P, D 1 ).…”

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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“…In terms of linear systems, this problem has been well solved for some different types of systems. For example, see [63,64,[72][73][74][76][77][78][79], etc. Compared with linear stochastic systems, the research on controllability of nonlinear stochastic systems has made slow progress, but many research results have also been achieved (e.g., [80][81][82][83][84][85][86][87]).…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Semilinear Stochastic Generalized Systems in Hilbert Spaces

2022

Mathematics

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Approximate controllability of two types of nonlinear stochastic generalized systems is investigated in the sense of mild solution in Hilbert spaces. Firstly, the approximate controllability of semilinear stochastic generalized systems with control only acting on the drift terms is discussed by GE-evolution operator and Nussbaum fixed-point theorem. Secondly, the approximate controllability of semilinear stochastic systems with control acting on both drift and diffusion terms is handled by using GE-evolution operator and Banach fixed-point theorem. At last, two illustrative examples are given.

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Moment observability and output feedback stabilisation for linear stochastic impulsive systems

Chen

Luo

Chen

2022

International Journal of Systems Science

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Controllability and observability of stochastic implicit systems and stochastic GE-evolution operator

Cited by 5 publications

References 26 publications

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

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

Approximate Controllability of Semilinear Stochastic Generalized Systems in Hilbert Spaces

Moment observability and output feedback stabilisation for linear stochastic impulsive systems

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