Observer-based fixed-time-synchronized control for uncertain Euler–Lagrange systems with bias–actuator faults

This article investigates the issue of observer-based fixed-time-synchronized tracking control for Euler-Lagrange (EL) systems with uncertain dynamics, bias-actuator faults and external disturbances. A novel fixed-time observer is proposed to reconstruct the actuator faults and system uncertainties, so that the observation error can reduce to zero within a fixed time. A fixed-time stable system with fast convergence rate is developed by using switching terms to design a newly sliding mode variable with the norm-normalized sign function. Then, on the basis of the reconstructed information from the fixed-time observer and the sliding mode variable, a robust control law is developed to realize fixed-time-synchronized stability of the EL system. It is concluded by Lyapunov stability theorem that the proposed method not only can guarantee that the boundary of convergence time is irrelevant of initial values of the system states, but also make all elements of the system tracking errors reach the origin simultaneously under the influence of actuator faults, external disturbances and uncertain dynamics. Finally, several comparative simulations are carried out to validate the developed observation and control schemes as well as their effectiveness.