Probabilistic universal learning networks and their applications to nonlinear control systems

Probabilistic Universal Learning Networks (PrULNs) are proposed, which are learning networks with a capability of dealing with stochastic signals. 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. A generalized learning algorithm has been devised for ULNs which can also be used in a unified manner for almost all kinds of learning networks. However, the ULNs can not deal with stochastic variables. Specific value of a stochastic signal can be propagated through a ULN, but the ULN does not provide any stochastic characteristics of the signals propagating through it. The PrULNs proposed here 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. The PrULNs will contribute to the solution of the following problems: (1) improving the generalization capability of the learning networks, (2) more sophisticated stochastic control than the conventional stochastic control, (3) designing problems for the complex systems such as chaotic systems. In this paper, PrULN is proposed and is applied to a nonlinear control system with noise.