A note for discrete time feedback control for stochastic systems driven by G-Brownian motion

Abstract

In this paper, we investigate the mean square and quasi-sure exponential stabilization of stochastic differential equations driven by G-Brownian motion, leveraging discrete-time feedback observations. We introduce a discrete-time feedback control mechanism within the drift part and demonstrate the existence of a threshold $\bar{\tau}>0$. This threshold ensures the stability of the controlled system for any discrete step size 𝜏 that is less than $\bar{\tau}$. To validate our control strategy, we present an illustrative example.

Keywords

G-Brownian motion / Discrete-time feedback / Stability

Acknowledgements

This work is supported in part by the NSFC (Grant Nos. 12571164 and 12171084), the Jiangsu Provincial Scientific Research Center of Applied Mathematics (Grant No. BK20233002), the fundamental Research Funds for the Central Universities (Grant No. RF1028623037), Jiangsu Key Lab for NSLSCS (Grant No. 202003), the Jiangsu Center for Collaborative Innovation in Geographical Information Resource and Applications, the Research Foundation of JinLing Institute of Technology (Grant No. Jit-b-201836), the Incubation Project of JinLing Institute of Technology (Grant No. Jit-fhxm-2021).

We would like to thank two anonymous referees for their constructive and helpful comments.

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