Nonlinear process identification using decision theory

This paper presents a learning technique for obtaining a model of a finite memory nonlinear process using only the input-output operating record. The model obtained simulates the process cause-effect relationship rather than the detailed structure of the process. As such, it is a "black box" model which can be used as a fast-time model for least-time control of the process. The learning technique used is similar to the technique of feature detection used in pattern recognition. Certain features of the input waveform
\alpha_{1}, \alpha_{2}, ... , \alpha_{N}
are observed, along with the quantized output levels
y_{1}, y_{2}, ... , y_{m}
. From these observations the lower-order probability distributions
P[\alpha_{j}/y_{i}]
are obtained. These lower-order probability distributions are used to approximate the higher-order distributions
P(\alpha_{1}, \alpha_{2}, ... , \alpha_{N}, y_{i})
. By incorporating these higher-order distributions into the equations of decision theory, the process output for a given input can be obtained.