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

• Published in: IEEE transactions on automatic control Vol. 66; no. 3; pp. 1306 - 1313
• Main Authors: Min, Huifang, Xu, Shengyuan, Zhang, Zhengqiang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• 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
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.2990173

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.