Identification of nonlinear dynamic systems by using Probabilistic Universal Learning Networks

In this paper, a method for identifying nonlinear dynamic systems with noise is proposed by using Probabilistic Universal Learning Networks (PrULNs). PrULNs are extensions of Universal Learning Networks (ULNs). ULNs form a superset of neural networks and were proposed to provide a universal framework for modeling and control of nonlinear large-scale complex systems. But the ULN does not provide any stochastic characteristics of the signals propagating through it. The PrULNs are equipped with machinery to calculate stochastic properties of signals and to train network parameters so that the signals behave with the pre-specified stochastic properties. On the other hand, it is generally recognized that there exists an overfitting problem when identification of nonlinear dynamic systems with noise is done by neural networks. In this paper, it is shown from simulation results of identification of a nonlinear robot dynamics that PrULNs are useful for avoiding the overfitting.