Relationship between levels of persistent excitation, architectures of neural networks and deterministic learning performance

Based on the concept of persistent excitation (PE), a deterministic learning algorithm is proposed for neural network (NN)-based identification of nonlinear systems recently. This paper investigates the quantitative relationship between the PE levels (including the level of excitation), the architectures of NNs and the convergence properties of deterministic learning, which is motivated by a practical problem of how to construct the NNs in order to guarantee sufficient level of excitation and identification accuracy for specific system trajectories. The results on PE levels are utilized to analyze the deterministic learning performance. It is proven that by increasing the density of NN centers, the approximation capabilities of NNs increase but the level of excitation decreases, which means that a trade-off exists in the convergence accuracy when adjusting NN architectures.