Controllability and Observability of Stochastic Singular Systems in Banach Spaces

Ge, Zhaoqiang

doi:10.1007/s11424-021-0164-7

Cited by 5 publications

(1 citation statement)

References 20 publications

(30 reference statements)

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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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Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Semilinear Stochastic Generalized Systems in Hilbert Spaces

2022

Mathematics

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Controllability and observability for some forward stochastic complex degenerate/singular Ginzburg–Landau equations

Yu¹,

Zhao²

2023

ESAIM: COCV

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This paper is addressed to establishing controllability and observability for some forward stochastic complex degenerate/singular Ginzburg-Landau equations. It is sufficient to establish appropriate observability inequalities for the corresponding backward and forward equations. The key is to prove the Carleman estimates of the forward and backward stochastic complex degenerate/singular Ginzburg-Landau operators. Compared with the existing deterministic results, it is necessary to overcome the difficulties caused by some complex coefficients and random terms. The results obtained cover those of deterministic cases and generalize those of stochastic degenerate parabolic equations. Moreover, the limit behavior of the coefficients in the equation is discussed.

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On the controllability and observability of fractional proportional linear systems

Bukhsh

Younus

2023

International Journal of Systems Science

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Controllability and Observability of Stochastic Singular Systems in Banach Spaces

Cited by 5 publications

References 20 publications

Approximate Controllability of Semilinear Stochastic Generalized Systems in Hilbert Spaces

Approximate Controllability of Semilinear Stochastic Generalized Systems in Hilbert Spaces

Controllability and observability for some forward stochastic complex degenerate/singular Ginzburg–Landau equations

On the controllability and observability of fractional proportional linear systems

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