Affection of the multi-branch number of universal learning networks on network structure

Abstract

Most systems in the field of modern control contain nonlinear parts. These nonlinear systems do not take on homogeneity and superposition. When we identify a nonlinear system, the traditional method is to linearize the system first, and then use the linear system to make an identification of the nonlinear system. In order to linearize the system, much information about the system is needed, such as the structure and the order of the system, but as control systems become more and more complicated, it becomes very difficult to get much information about the system, so the shortcomings of such a method are becoming more and more notable. An artificial neural network has the ability to approximate the nonlinear function to any extent, so it provides a new method of system identification. However, the present neural networks also have shortcomings: first, their structure becomes too large and too loose as the system becomes more complicated, and secondly, the time delay is non-arbitrary. To solve such problems, this paper proposes a universal learning network (ULN). This network has the following characteristics: (1) all of the nodes are connected to each other; (2) there are multiple branches between every pair of nodes; (3) an arbitrary time delay can be set on every branch; and (4) there is a switching function on every branch. The switching function is used to delete unnecessary nodes and branches, to make the network simple. The learning algorithm of the network uses ordered derivatives and learning based on the gradient decent algorithm. In using a ULN to identify a nonlinear dynamical system, it can be proved that this network has excellent learning and generalization abilities, and also the network can be made compact.