Data-Driven Anti-Disturbance Control with High-Order Extended State Observer for Unknown Nonlinear Systems

For nonlinear systems with unknown dynamics subject to external disturbances, a data-driven anti-disturbance control scheme is proposed by using only the measured system input and output data. A modified local compact-form dynamic linearization (CFDL) model is firstly established for the considered system. Then, a predictive anti-disturbance control law is designed by solving a constrained optimization problem in time domain. To make the control law implementable, the pseudo partial derivative (PPD) of the above model at the future time step is estimated by leveraging an auto-regressive prediction algorithm with the past PPD estimations. The residual disturbance to be predicted is constructed by using the current-time disturbance and its high-order difference estimated by an extended state observer (ESO). The convergence of the PPD estimation, ESO and the tracking error is analyzed with proofs. Finally, an illustrative example is given to validate the effectiveness and advantages of the proposed design over the existing methods.