In this article, we present an adaptive prescribed-time control method for a class of nonlinear telerobotic systems with actuator faults and position error constraints. Extended from prescribed-time stability, practically prescribed-time stability (PPTS) is proposed for the first time aiming at stability analysis and control synthesis of nonlinear systems with disturbance and uncertainty. We show that, under the control scheme in the framework of PPTS, the system states are guaranteed to converge to a user-defined set (physically realizable) within user-defined settling time (physically realizable). Based on PPTS, an adaptive fault-tolerant controller is developed by integrating a novel exponential-type barrier Lyapunov function. Rigorous stability analysis based on back-stepping approach proves that, under the proposed control strategy, synchronization errors converge to a user-defined residual-set within predefined settling time and never exceed the prescribed range. Universal performance indexes, including the settling time, residual-set, accuracy, and overshoot, can be user-defined and only dependent on fewer user-defined parameters. Simulation results illustrate the effectiveness of the developed control scheme.

中文翻译：

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具有位置误差约束的远程操作系统的自适应容错规定时间控制


在本文中，我们提出了一种针对具有执行器故障和位置误差约束的一类非线性远程机器人系统的自适应规定时间控制方法。在规定时间稳定性的基础上，首次提出了实用规定时间稳定性（PPTS），针对具有扰动和不确定性的非线性系统的稳定性分析和控制综合。我们表明，在 PPTS 框架的控制方案下，系统状态保证在用户定义的稳定时间内（物理上可实现）收敛到用户定义的集合（物理上可实现）。基于PPTS，集成新型指数型势垒Lyapunov函数，开发了自适应容错控制器。基于反步方法的严格稳定性分析证明，在所提出的控制策略下，同步误差在预定义的稳定时间内收敛到用户定义的残差集，并且永远不会超过规定的范围。通用性能指标，包括稳定时间、残差设定、精度和超调，可以由用户定义，并且仅依赖于较少的用户定义参数。仿真结果说明了所开发控制方案的有效性。