Abstract
Realization of multi-dimensional separating surfaces is one of the current problems in the field of time-optimal control as well as in the field of pattern classification. Some structures of a multi-dimensional function generator which can be employed in pattern-classifying problems and optimal control problems are proposed in this paper. The function generators are composed of two kinds of threshold elements, relay and limiter element. A 2-layered network of threshold elements is useful to generate a function which can be expressed by a sum of nonlinear functions of a linear combination of input variables. Functions of more general form can be generated by dividing the variable space into many convex regions and assigning a hyperplane to each region. In this method, analog AND and analog OR operations are necessary to connect those hyperplanes. Furthermore, the number of threshold elements required to realize a function can be diminished, if the information about convexity of the function is available. The number of threshold elements required to realize an n-dimensional function is also given in this paper.
