Adaptive feedforward RBF neural network control with the deterministic persistence of excitation

Based on the partial persistence of excitation (PE), the recent deterministic learning theory of adaptive RBF neural network (RBFNN) control can just guarantee that the partial weights of RBFNNs converge to their optimal values. This paper proposes two kinds of adaptive feedforward RBFNN control frameworks with a more deterministic learning mechanism: the reduced lattice scheme and the optimized scheme. Specifically, the RBFNNs satisfy a standard PE condition and the PE levels are deterministic. The reduced lattice scheme removes the insignificant hidden nodes from the lattice scheme, whereas the optimized scheme calculates the distribution of hidden nodes to optimally distribute along the desired trajectory by the K-means algorithm. Under the proposed method, the weights of all the hidden nodes converge to their optimal values, while a deeper insight on the convergence rate of the weights of the RBFNN is drawn. Comparative simulation experiments demonstrate that the optimized scheme outperforms both the reduced lattice scheme and the traditional lattice scheme from the perspectives of both the approximate performance and the PE level. Furthermore, when the sampling frequency is low, both the optimized and reduced lattice schemes achieve better tracking performance than the model-based scheme.