RBFNN-Based ADRC Design for Continuous-Time Systems with Unknown Nonlinear Dynamics Subject to Time-Varying Disturbance

In this paper, a radial basis function neural network (RBFNN) based active disturbance rejection control (ADRC) scheme is proposed for continuous-time systems with unknown nonlinear dynamics and time-varying disturbance. By using RBFNN to online approximate the unknown nonlinear dynamics, a novel nonlinear extended state observer (ESO) is firstly designed to estimate the total disturbance consisting of time-varying external disturbance and RBFNN approximation error. Then, an anti-disturbance feedback control law together with a tracking differentiator is designed to counteract the total disturbance in a feedforward manner. The bounded convergence of the closed-loop system and ESO as well as the estimation errors of the weighting vector are rigorously analyzed based on the Lyapunov stability theory. A case study is carried out to demonstrate the effectiveness and merit of the proposed design, in contrast to the conventional ADRC.