This paper examines the adaptive control of high-order nonlinear systems with strict-feedback form. An adaptive fixed-time control scheme is designed for nonlinear systems with unknown uncertainties. In the design process of a backstepping controller, the Lyapunov function, an effective controller, and adaptive law are constructed. Combined with the fixed-time Lyapunov stability criterion, it is proved that the proposed control scheme can ensure the stability of the error system in finite time, and the convergence time is independent of the initial condition. Finally, simulation results verify the effectiveness of the proposed control strategy.

中文翻译：

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严格反馈高阶非线性系统的自适应固定时间控制

本文研究了具有严格反馈形式的高阶非线性系统的自适应控制。自适应固定时间控制方案是为具有未知不确定性的非线性系统设计的。在反步控制器的设计过程中，构建了李雅普诺夫函数、有效控制器和自适应律。结合固定时间Lyapunov稳定性判据，证明了所提出的控制方案能够保证误差系统在有限时间内的稳定性，且收敛时间与初始条件无关。最后，仿真结果验证了所提出的控制策略的有效性。