A functions localized neural network with branch gates
Neural Networks
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Universal learning networks (ULNs) and robust control system design are discussed, ULNs provide a generalized framework to model and control complex systems. They consist of a number of interconnected nodes where the nodes may have any continuously differentiable nonlinear functions in them and each pair of nodes can be connected by multiple branches with arbitrary time delays. Therefore, physical systems which can be described by differential or difference equations and also their controllers can be modeled in a unified way. So, ULNs constitute a superset of neural networks or fuzzy neural networks. In order to optimize the systems, a generalized learning algorithm is derived for the ULNs, in which both the first order derivatives (gradients) and the higher order derivatives are incorporated. The derivatives are calculated by using forward or backward propagation schemes. These algorithms for calculating the derivatives are extended versions of back propagation through time (BPTT) and real time recurrent learning (RTRL) by Williams in the sense that generalized nonlinear functions and higher order derivatives are dealt with. As an application of ULNs, the higher order derivative, one of the distinguished features of ULNs, is applied to realizing a robust control system in this paper. In addition, it is shown that the higher order derivatives are effective tools to realize sophisticated control of nonlinear systems. Other features of ULNs such as multiple branches with arbitrary time delays and using a priori information will be discussed in other papers