The way of propagating and control of stochastic signals through Universal Learning Networks (ULNs) and its applications are proposed. ULNs have been already developed to form a superset of neural networks and have been applied as a universal framework for modeling and control of non-linear large-scale complex systems. However, the ULNs cannot deal with stochastic variables. Deterministic signals can be propagated through a ULN, but the ULN does not provide any stochastic characteristics of the signals propagating through it. The proposed method named Probabilistic Universal Learning Networks (PrULNs) can process stochastic variables and can train network parameters so that the signals behave with the pre-specified stochastic properties. As examples of applications of the proposed method, control and identification of non-linear dynamic systems with noises are studied, and it is shown that the method are useful for dealing with the control and identification of the non-linear stochastic systems contaminated with noises.
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