Adaptive Finite-Time Stabilization of Stochastic Nonlinear Systems Subject to Full-State Constraints and Input Saturation

In this article, the adaptive finite-time tracking control is studied for state constrained stochastic nonlinear systems with parametric uncertainties and input saturation. To this end, a definition of semiglobally finite-time stability in probability (SGFSP) is presented and a related stochastic Ly...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2021-03, Vol.66 (3), p.1306-1313
Main Authors: Min, Huifang, Xu, Shengyuan, Zhang, Zhengqiang
Format: Article
Language:English
Subjects:
Adaptive control
Adaptive finite-time control
Adaptive systems
Approximation
Backstepping
barrier Lyapunov function (BLF)
Constraints
Feedback control
full-state constraints
input saturation
Liapunov functions
Lyapunov methods
Nonlinear systems
Reference signals
Saturation
semi-globally finite-time stability in probability (SGFSP)
Stability analysis
stochastic nonlinear systems
Stochastic processes
Stochastic systems
Theorems
Tracking control
Uncertainty
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Summary:In this article, the adaptive finite-time tracking control is studied for state constrained stochastic nonlinear systems with parametric uncertainties and input saturation. To this end, a definition of semiglobally finite-time stability in probability (SGFSP) is presented and a related stochastic Lyapunov theorem is established and proved. To alleviate the serious uncertainties and state constraints, the adaptive backstepping control and barrier Lyapunov function are combined in a unified framework. Then, by applying a function approximation method and the auxiliary system method to deal with input saturation respectively, two adaptive state-feedback controllers are constructed. Based on the proposed stochastic Lyapunov theorem, each constructed controller can guarantee the closed-loop system achieves SGFSP, the system states remain in the defined compact sets and the output tracks the reference signal very well. Finally, a stochastic single-link robot system is established and used to demonstrate the effectiveness of the proposed schemes.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2020.2990173