Fixed-Time Stabilization of a Class of Stochastic Nonlinear Systems

This paper investigates an improved fixed-time stability theory together with a state feedback controller for a class of nonlinear stochastic systems. First, a delicate transformation is performed, and next, a Gamma function is utilized to directly derive the value of the integral function, which ul...

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Bibliographic Details
Published in:Actuators 2024-01, Vol.13 (1), p.3
Main Authors: Long, Zhenzhen, Zhou, Wen, Fang, Liandi, Zhu, Daohong
Format: Article
Language:English
Subjects:
adding a power integrator
Amplification
Control systems
Controllers
Equilibrium
Feedback control
fixed-time stability
Gamma function
Nonlinear systems
Simulation methods
Stabilization
State feedback
state feedback control
stochastic nonlinear system
Stochastic systems
Upper bounds
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Summary:This paper investigates an improved fixed-time stability theory together with a state feedback controller for a class of nonlinear stochastic systems. First, a delicate transformation is performed, and next, a Gamma function is utilized to directly derive the value of the integral function, which ultimately yields a fixed-time stabilization theorem with a higher precision upper bound for the settling time. Unlike the existing estimation process of amplifying twice, we only performed one amplification, which weakens the effect of amplification. Then, a state feedback controller is constructed for stochastic systems by the method of adding a power integrator. Utilizing the proposed stochastic fixed-time stability theory, simulations show that the intended controller ensures that the trivial solution of the suggested system is fixed-time stable in probability. The results of the simulation demonstrate that the suggested control scheme is meaningful.
ISSN:2076-0825
2076-0825
DOI:10.3390/act13010003