Search for optimal time delays in universal learning network

Universal Learning Network(U.L.N.), which can model and control the large scale complicated systems naturally, consists of nonlinearly operated nodes and multi-branches that may have arbitrary time delays including zero or minus ones. Therefore, U.L.N. can be applied to many kinds of systems which are difficult to be expressed by ordinary first order difference equations with one sampling time delay. It has been already reported that learning algorithm of parameter variables in U.L.N. by forward and backward propagation is useful for modeling, managing and controlling of the large scale complicated systems such as industrial plants, economic, social and life phenomena. But, in the previous learning algorithm of U.L.N., time delays between the nodes were fixed, in other words, criterion function of U.L.N. was improved by adjusting only parameter variables. In this paper, a new learning algorithm is proposed, where not only parameter variables but also time delays between the nodes can be adjusted. Because time delays are integral numbers, adjustment of time delays can be carried out by a kind of random search procedure which executes intensified and diversified search in a single framework.