Deterministic Learning-Based Robust Practical Output Regulation for Second-Order Nonlinear Systems

This article intends to investigate the semi-global robust practical output regulation problem for a class of second-order nonlinear systems with parametric and non-parametric uncertainties based on deterministic learning method. First, by constructing the internal models, the robust output regulation problem is transformed into the semi-global robust practical stabilization problem. Second, we propose an adaptive neural control (ANC) strategy to solve the stabilization problem and utilize the radial basis function neural networks (RBF NNs) to identify unknown dynamic. Moreover, under the persistently exciting (PE) property, the unknown dynamics can be identified and the learned knowledge is saved as some constant NN weights. Finally, we design an deterministic learning-based adaptive neural control (DLANC) law with the learned knowledge to solve the output regulation problem and improve control performance.