Neural Network-based e-Adaptive Dynamic Programming and e-Optimal Control for Nonlinear Systems

Abstract

By applying a novel e-optimal control performance index function as an approximation of the optimal performance index function, the e-optimal control theory and e-adaptive dynamic programming algorithms are established. The e-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 e-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 e-adaptive dynamic programming, which is an improvement of the radial basis function neural network (RBFNNs) and the wavelet neural network (WNN).