Correspondence Farshad Khorrami, Control/Robotics Research Laboratory, Department of ECE, NYU Tandon School of Engineering, Brooklyn, NY, USA. Email: khorrami@nyu.edu Summary The prescribed-time output-feedback stabilization (ie, regulation of the state and control input to zero within a “prescribed” time picked by the control designer irrespective of the initial state) of a general class of uncertain nonlinear strict-feedback-like systems is considered. Unlike prior results, the class of systems considered in this article allows crossproducts of unknown parameters (without any required magnitude bounds on unknown parameters) and unmeasured state variables in uncertain state-dependent nonlinear functions throughout the system dynamics. We show that prescribed-time output-feedback stabilization (ie, both prescribed-time state estimation and prescribed-time regulation) is achieved through a novel output-feedback control design involving specially designed dynamics of an adaptation state variable and a high-gain scaling parameter in combination with a temporal transformation and a dual high-gain scaling based observer and controller design. While standard dynamic adaptation techniques cannot be applied due to crossproducts of unknown parameters and unmeasured states, we show that instead, the dynamics of the high-gain scaling parameter and adaptation parameter can be designed with temporal forcing terms to ensure that unknown parameters in system dynamics are dominated by a particular fractional power of the high-gain scaling parameter and the adaptation parameter after a subinterval (of unknown length) of the prescribed time interval. We show that the control law can be designed such that the system state and input are regulated to zero in the remaining subinterval of the prescribed time interval.

中文翻译：

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具有未知参数和未测量状态的非线性系统在规定时间内的自适应输出反馈稳定

通讯作者 Farshad Khorrami，美国纽约布鲁克林纽约大学坦登工程学院 ECE 系控制/机器人研究实验室。电子邮件：khorrami@nyu.edu 总结 规定时间输出反馈稳定（即，在控制设计者选择的“规定”时间内将状态和控制输入调节为零，而不管初始状态如何）考虑了不确定的非线性严格反馈类系统。与先前的结果不同，本文中考虑的系统类别允许在整个系统动力学中的不确定状态相关非线性函数中的未知参数（对未知参数没有任何要求的幅度界限）和未测量状态变量的交叉积。我们证明了规定时间的输出反馈稳定性（即，规定时间状态估计和规定时间调节）是通过一种新颖的输出反馈控制设计实现的，该设计涉及专门设计的自适应状态变量和高增益缩放参数的动态，结合时间变换和双高增益基于缩放的观察器和控制器设计。虽然由于未知参数和未测量状态的叉积而无法应用标准动态自适应技术，但我们表明，高增益缩放参数和自适应参数的动态可以用时间强制项来设计，以确保系统动力学中的未知参数在规定的时间间隔的子间隔（未知长度）之后，由高增益缩放参数和自适应参数的特定分数功率支配。