School of Computer Engineering, City Institute, Dalian University of Technology, Dalian 116000, China.
School of Management, Dalian University of Finance and Economics, Dalian 116000, China.
Math Biosci Eng. 2022 Jul 26;19(10):10637-10655. doi: 10.3934/mbe.2022497.
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.
本文针对一类多输入多输出（MIMO）耦合非线性系统，尝试设计一种有限时间自适应模糊反步控制方案，系统状态不可测。针对系统的不确定性，采用自适应模糊逻辑系统（AFLS）逼近系统的不确定性，利用有限时间扩张状态观测器（FT-ESO）估计系统的不可测状态，其中观测器的状态是一个以系统状态为中心的球体。通过反步和有限时间理论的结合，保证了控制效果的准确性和效率。通过有限时间 Lyapunov 稳定性定理证明，闭环自适应控制系统的所有状态均具有半全局实用有限时间稳定性（SGPFS），系统状态的跟踪误差在有限时间内收敛到原点的一个小邻域内。通过仿真验证了该方案的有效性。
