Universal learning network and its application to chaos control

Universal Learning Networks (ULNs) are proposed and their application to ch aos control is discussed. ULNs provide a generalized framework to model and control complex systems. They consist of a number of inter-connected nodes where the nodes may have any continuously differentiable nonlinear functio ns in them and each pair of nodes can be connected by multiple branches wit h arbitrary time delays. Therefore, physical systems, which can be describe d by differential or difference equations and also their controllers, can b e modeled in a unified way, and so ULNs may form a super set of neural netw orks and fuzzy neural networks. In order to optimize the ULNs, a generalize d learning algorithm is derived, in which both the first order derivatives (gradients) and the higher order derivatives are incorporated. The derivati ves are calculated by using forward or backward propagation schemes. These algorithms for calculating the derivatives are extended versions of Back Pr opagation Through Time (BPTT) and Real Time Recurrent Learning (RTRL) of Wi lliams in the sense that generalized node functions, generalized network co nnections with multi-branch of arbitrary time delays, generalized criterion functions and higher order derivatives can be deal with. As an application of ULNs, a chaos control method using maximum Lyapunov exponent of ULNs is proposed. Maximum Lyapunov exponent of ULNs can be formulated by using hig her order derivatives of ULNs, and the parameters of ULNs can be adjusted s o that the maximum Lyapunov exponent approaches the target value. From the simulation results, it has been shown that a fully connected ULN with three nodes is able to display chaotic behaviors. (C) 2000 Elsevier Science Ltd. All rights reserved.