Observer-based finite-time adaptive fuzzy back-stepping control for MIMO coupled nonlinear systems

Chao Wang; Cheng Zhang; Dan He; Jianliang Xiao; Liyan Liu; Chao Wang; Cheng Zhang; Dan He; Jianliang Xiao; Liyan Liu

doi:10.3934/mbe.2022497

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 10: 10637-10655. doi: 10.3934/mbe.2022497

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Observer-based finite-time adaptive fuzzy back-stepping control for MIMO coupled nonlinear systems

1.
School of Computer Engineering, City Institute, Dalian University of Technology, Dalian 116000, China
2.
School of Management, Dalian University of Finance and Economics, Dalian 116000, China

Academic Editor: Xiaodi Li

Received: 11 May 2022 Revised: 18 July 2022 Accepted: 18 July 2022 Published: 26 July 2022

An attempt is made in this paper to devise a finite-time adaptive fuzzy back-stepping control scheme for a class of multi-input and multi-output (MIMO) coupled nonlinear systems with immeasurable states. In view of the uncertainty of the system, adaptive fuzzy logic systems (AFLSs) are used to approach the uncertainty of the system, and the unmeasured states of the system are estimated by the finite-time extend state observers (FT-ESOs), where the state of the observer is a sphere around the state of the system. The accuracy and efficiency of the control effect are ensured by combining the back-stepping and finite-time theory. It is proved that all the states of the closed-loop adaptive control system are semi-global practical finite-time stability (SGPFS) by the finite-time Lyapunov stability theorem, and the tracking errors of the system states converge to a tiny neighborhood of the origin in a finite time. The validity of this scheme is demonstrated by a simulation.
- coupled nonlinear systems,
- adaptive fuzzy logic system,
- extended state observer,
- back-stepping,
- finite time
Citation: Chao Wang, Cheng Zhang, Dan He, Jianliang Xiao, Liyan Liu. Observer-based finite-time adaptive fuzzy back-stepping control for MIMO coupled nonlinear systems[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 10637-10655. doi: 10.3934/mbe.2022497

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Abstract

An attempt is made in this paper to devise a finite-time adaptive fuzzy back-stepping control scheme for a class of multi-input and multi-output (MIMO) coupled nonlinear systems with immeasurable states. In view of the uncertainty of the system, adaptive fuzzy logic systems (AFLSs) are used to approach the uncertainty of the system, and the unmeasured states of the system are estimated by the finite-time extend state observers (FT-ESOs), where the state of the observer is a sphere around the state of the system. The accuracy and efficiency of the control effect are ensured by combining the back-stepping and finite-time theory. It is proved that all the states of the closed-loop adaptive control system are semi-global practical finite-time stability (SGPFS) by the finite-time Lyapunov stability theorem, and the tracking errors of the system states converge to a tiny neighborhood of the origin in a finite time. The validity of this scheme is demonstrated by a simulation.

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