Uncertainty Predictive Observer-Based Model-Free Adaptive Disturbance Rejection Control

An uncertainty predictive observer-based model-free adaptive disturbance rejection control (UPO-MFADRC) is developed for nonaffine nonlinear systems with uncertain nonlinearities and exogenous disturbances. A linear predictive data model (LPDM) consisting of a linear parametric part and a total residual uncertainty is derived from the original nonaffine nonlinear system. Then, an adaptive law with a prediction algorithm is proposed to address the unknown parameter sequence of the LPDM. An uncertainty predictive observer (UPO) is developed to predict the future behavior of the total residual uncertainty sequence of the LPDM including the unmodeled dynamics and exogenous disturbances. The UPO involves an extended state observer for the uncertainty estimation at the current time instant and a hierarchical prediction algorithm to predict the uncertainty at more than one future time instant. Finally, an entire UPO-MFADRC is constructed by incorporating the adaptive law, UPO, and a control law generated from the moving-window optimization of a designed performance index function. The proposed UPO-MFADRC is almost model-independent except that the control direction needs to be known. The convergence is shown mathematically with the use of contraction mapping-based method. Simulation verifies the ability of the proposed UPO-MFADRC in tolerating the uncertainty.