Robust adaptive neural practical fixed-time tracking control for uncertain Euler-Lagrange systems under input saturations

Abstract This paper develops a robust adaptive neural practical fixed-time tracking control scheme for Euler-Lagrange systems (ELSs) with unknown dynamics and external disturbances under input saturations. A novel auxiliary dynamic system governed by a smooth piecewise continuous function is constructed to handle the input saturation effect, while promoting to achieve the fixed-time convergence of tracking errors. Moreover, the unknown dynamics of ELSs and the bound vector of unknown external disturbances are synthesized into a compounded uncertain vector in this paper. Here, adaptive neural networks with the ∊-modification updating laws are employed to only approximate the compounded uncertain vector, rather than each dynamic matrix of ELSs, such that the computational burden of the developed control scheme is significantly reduced. It is theoretically proven that the trajectory tracking is able to be achieved in a fixed time under the developed adaptive neural tracking control scheme, while all signals in the Euler-Lagrange closed-loop tracking control system are bounded. The simulation results on a 2-link robotic manipulator are included to illuminate the effectiveness of our developed tracking control scheme and superiority to a finite-time control scheme.