Adaptive Fault-Tolerant Prescribed-Time Control for Teleoperation Systems With Position Error Constraints

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.