Abstract
A practical fixed-time adaptive fuzzy control strategy is investigated for uncertain nonlinear systems with time-varying asymmetric constraints and input quantization. To overcome the difficulties of designing controllers under the state constraints, a unified barrier function approach is employed to construct a coordinate transformation that maps the original constrained system to an equivalent unconstrained one, thus relaxing the time-varying asymmetric constraints upon system states and avoiding the feasibility check condition typically required in the traditional barrier Lyapunov function based control approach. Meanwhile, the “explosion of complexity” problem in the traditional backstepping approach arising from repeatedly derivatives of virtual controllers is solved by using the command filter method. It is verified via the fixed-time Lyapunov stability criterion that the system output can track a desired signal within a small error range in a predetermined time, and that all system states remain in the constraint range. Finally, two simulation examples are offered to demonstrate the effectiveness of the proposed strategy.
摘要
研究了具有时变不对称约束和输入量化的不确定非线性系统, 提出一种实际固定时间自适应模糊控制方法. 为消除状态约束对控制器设计的影响, 采用一个统一的障碍函数方法将原有约束系统映射为无约束系统, 这不仅放松了时变非对称约束对系统状态的限制, 而且避免了传统的障碍Lyapunov函数控制方法中的可行性条件检查. 同时, 利用命令滤波方法解决了传统反步法中的“复杂度爆炸”问题. 通过固定时间Lyapunov稳定性判据, 证实系统输出能够在预定时间内以较小误差范围跟踪参考信号, 并且系统的所有状态保持在约束范围内. 最后, 通过2个仿真实例验证了所提方法的有效性.
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Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
The authors gratefully acknowledge the technical and financial support provided by the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.
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Ben NIU supervised the project. Zixuan HUANG performed numerical simulations. Adil M. AHMAD accomplished experimental verification. Zixuan HUANG drafted the paper. Huanqing WANG helped organize the paper. Xudong ZHAO revised and finalized the paper.
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Project supported by Institutional Fund Projects (No. IFPIP: 131-611-1443)
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Huang, Z., Wang, H., Niu, B. et al. Practical fixed-time adaptive fuzzy control of uncertain nonlinear systems with time-varying asymmetric constraints: a unified barrier function based approach. Front Inform Technol Electron Eng 25, 1282–1294 (2024). https://doi.org/10.1631/FITEE.2300408
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DOI: https://doi.org/10.1631/FITEE.2300408
Key words
- Unified barrier function
- Time-varying asymmetric state constraints
- Fuzzy logic systems
- Fixed-time control
- Command filter