| By applying a novel epsilon-optimal control performance index function as an approximation of the optimal performance index function, the epsilon-optimal control theory and epsilon-adaptive dynamic programming algorithms are established. The epsilon-optimal control theory provides a new sense to overcome the "curse of dimensionality" problem and the "over optimal" problem of the optimal control theory. An algorithm of epsilon-adaptive dynamic programming for discrete time systems using neural networks is given for general nonlinear system as well as a fast iterated algorithm is designed for the case that the utility function is quadratic. Furthermore, a novel wavelet basis function neural network (WBFNN) is defined for sequential learning during the numerical simulations of epsilon-adaptive dynamic programming, which is an improvement of the radial basis function neural network (RBFNNs) and the wavelet neural network (WNN). |
