Guaranteeing Global Stability for Neuro-Adaptive Control of Unknown Pure-Feedback Nonaffine Systems via Barrier Functions

Most existing approximation-based adaptive control (AAC) approaches for unknown pure-feedback nonaffine systems retain a dilemma that all closed-loop signals are semiglobally uniformly bounded (SGUB) rather than globally uniformly bounded (GUB). To achieve the GUB stability result, this article pres...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2023-09, Vol.34 (9), p.5869-5881
Main Authors: Liu, Yong-Hua, Liu, Yu-Fa, Su, Chun-Yi, Liu, Yang, Zhou, Qi, Lu, Renquan
Format: Article
Language:English
Subjects:
Adaptive control
Approximation
Artificial neural networks
Automation
Backstepping
Barrier function
Closed loops
Differential calculus
Feedback
Feedback control
global stability
Liapunov functions
Mathematical analysis
Neural networks
neuro-adaptive control
Nonlinear systems
pure-feedback nonaffine systems
Stability criteria
Trajectory
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Summary:Most existing approximation-based adaptive control (AAC) approaches for unknown pure-feedback nonaffine systems retain a dilemma that all closed-loop signals are semiglobally uniformly bounded (SGUB) rather than globally uniformly bounded (GUB). To achieve the GUB stability result, this article presents a neuro-adaptive backstepping control approach by blending the mean value theorem (MVT), the barrier Lyapunov functions (BLFs), and the technique of neural approximation. Specifically, we first resort the MVT to acquire the intermediate and actual control inputs from the nonaffine structures directly. Then, neural networks (NNs) are adopted to approximate the unknown nonlinear functions, in which the compact sets for maintaining the approximation capabilities of NNs are predetermined actively through the BLFs. It is shown that, with the developed neuro-adaptive control scheme, global stability of the resulting closed-loop system is ensured. Simulations are conducted to verify and clarify the developed approach.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2021.3131364