Abstract

In this paper, a fixed-time adaptive fuzzy control scheme is investigated to stabilize a class of uncertain nonlinear systems with full-state constraints. A novel secant barrier Lyapunov function (SBLF) is first constructed to design the controller and obtain the fixed-time stability properties by using the (SBLF) in the design process of back-stepping. The adaptive controller is presented to guarantee that the tracking errors of the system can converge into the neighborhood around the equilibrium point in a fixed time and all the system states can be restricted within the predefined time-varying boundaries. By making use of Lyapunov analysis, we can prove that all the signals in the closed loop system are uniformly ultimately bounded and the output is well driven to follow the desired trajectory. Finally, simulations are given to verify the effectiveness of the method.

中文翻译：

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时变状态约束非线性系统的固定时间自适应模糊控制

摘要

本文研究了一种固定时间自适应模糊控制方案来稳定一类具有全状态约束的不确定非线性系统。首先构造了一种新颖的割线势垒Lyapunov函数(SBLF)来设计控制器，并在反步设计过程中利用(SBLF)获得了固定时间稳定性特性。提出自适应控制器以保证系统的跟踪误差在固定时间内收敛到平衡点周围的邻域内，并且所有系统状态都可以限制在预定的时变边界内。通过利用李亚普诺夫分析，我们可以证明闭环系统中的所有信号最终一致有界，并且输出被很好地驱动遵循期望的轨迹。最后通过仿真验证了该方法的有效性。