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Approximate Controllability of Semilinear Stochastic Generalized Systems in Hilbert Spaces

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  • Zhaoqiang Ge

    (School of Mathematics and Statistics, Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an 710049, China)

Abstract

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.

Suggested Citation

  • Zhaoqiang Ge, 2022. "Approximate Controllability of Semilinear Stochastic Generalized Systems in Hilbert Spaces," Mathematics, MDPI, vol. 10(17), pages 1-30, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3050-:d:896460
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    References listed on IDEAS

    as
    1. Zhaoqiang Ge, 2021. "Review of the Latest Progress in Controllability of Stochastic Linear Systems and Stochastic GE-Evolution Operator," Mathematics, MDPI, vol. 9(24), pages 1-42, December.
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    Cited by:

    1. Zhaoqiang Ge, 2023. "Controllability of Semilinear Stochastic Generalized Systems in Hilbert Spaces by GE-Evolution Operator Method," Mathematics, MDPI, vol. 11(3), pages 1-26, February.

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