This paper aims to focus on handling the tracking problem of an input constrained uncertain Euler-Lagrange system (ELS) with prescribed performance and unknown external disturbance. An asymptotic control performance is presented. Furthermore, the estimator and adaptive control design, stability analysis and simulation on a robotic system are given in the paper.
A finite-time stability-based estimator is proposed to handle the problems arising from system uncertainty and external disturbance. An asymmetric barrier Lyapunov function-based approach is designed to address the problem of prescribed performance. The auxiliary variable is introduced to mitigate the impact of input constraints on system dynamics. Furthermore, the asymptotic stability of the system is proven by using the Lyapunov direct method.
According to the theoretical analysis and simulations, the uncertainty and disturbance estimator (UDE) can estimate uncertainty and disturbance accurately in a finite time. The UDE-based adaptive control is not only effective to guarantee the input and tracking performance within prescribed constraints, but also capable of driving the system to asymptotic stability. Furthermore, the proposed controller is proven to be effective for the robotic system through simulations.
UDE can handle disturbance and uncertainty of ELS simultaneously. In addition, the estimation errors achieve convergence in a finite time. Under the complex conditions with input and performance constraints, the UDE-based control method can make the tracking system asymptotically stable.
