Convergence analysis of continuous-time systems based on feedforward neural networks

In this paper, we construct a feedforward neural network (NN) based system containing two NNs. The convergence of the NN based system is analyzed in detail. For setting up the NN based system, an NN observer is first designed to estimate the system states. Then, based on the observed states, a feedforward neuro-control system is constructed by using adaptive dynamic programming (ADP). In this design, two NN structures are used: a three-layer feedforward NN to constitute the observer which can be applied to the systems with high degrees of nonlinearity and without a priori knowledge about system dynamics, and a critic NN to approximate the value function. Moreover, the weight update laws for the critic NN are generated using a gradient-descent method based on a modified temporal difference error, which is independent of the system dynamics. Finally, uniform ultimate boundedness (UUB) of the NN based system is proved.