Discrete-Time Adaptive Dynamic Programming using Wavelet Basis Function Neural Networks

Dynamic programming for discrete time systems is difficult due to the "curse of dimensionality": one has to find a series of control actions that must be taken in sequence, hoping that this sequence will lead to the optimal performance cost, but the total cost of those actions will be unknown until the end of that sequence. In this paper, we present our work on adaptive dynamic programming (ADP) for nonlinear discrete time system using neural networks. The neural network we adopted here is the wavelet basis function (WBF) neural network. We will exam the performance of an ADP algorithm using WBF neural networks. The comparison shows that when WBF neural networks are employed, the ADP algorithm gives faster training speed than when RBF neural networks are employed