Actuator faults often occur in physical systems, which seriously affect the transient performance and control accuracy of the system. For the finite-time consensus tracking problem of multiple Lagrangian systems with actuator faults and preset error constraints, a novel distributed fault-tolerant controller is proposed in this paper. The proposed controller is developed based on the barrier Lyapunov function method and the adding a power integrator technique, which can not only guarantee the steady-state performance of the system but also its transient performance. Due to its strong sensitivity to the variation of system errors, the proposed controller can quickly eliminate the system initial errors and the error perturbations caused by actuator faults. That is, the controller can guarantee that the consensus error converges to zero in a finite time and is always constrained within the preset error bound. Finally, the effectiveness of the developed controller is verified by simulation of a multi-manipulator system.

执行器故障经常发生在物理系统中，严重影响系统的瞬态性能和控制精度。针对具有执行器故障和预设误差约束的多个拉格朗日系统的有限时间一致性跟踪问题，本文提出了一种新型的分布式容错控制器。所提出的控制器是基于势垒李雅普诺夫函数法和添加功率积分器技术开发的，不仅可以保证系统的稳态性能，而且可以保证系统的瞬态性能。由于其对系统误差的变化具有很强的敏感性，所提出的控制器可以快速消除系统初始误差和执行器故障引起的误差扰动。那是，控制器可以保证共识误差在有限时间内收敛到零，并且始终约束在预设的误差范围内。最后，通过多机械手系统的仿真验证了所开发控制器的有效性。