Simulating the Fast Prediction Strategy of the Sensorimotor System

The values of a physiological parameter and its time derivatives, detected at different times by different sensory receptors, are processed by the sensorimotor system to predict the time evolution of the parameter and convey appropriate control commands acting with minimum latency (few milliseconds) from the sensory stimulus. We have derived a power-series expansion (U-expansion) to simulate the fast prediction strategy of the sensorimotor system. Given a time-function [Formula: see text] , a time-instant [Formula: see text] , and a time-increment [Formula: see text] , the U-expansion enables the calculation of [Formula: see text] from [Formula: see text] and the values [Formula: see text] of the derivatives [Formula: see text] of [Formula: see text] at arbitrarily different times [Formula: see text] , instead of time [Formula: see text] as in the Taylor series. For increments [Formula: see text] significantly greater than the maximum [Formula: see text] among the differences [Formula: see text] , the error associated with truncation of the U-expansion at a given order closely equalizes the error of the corresponding Taylor series ([Formula: see text]) truncated at the same order. Small values of [Formula: see text] and higher values of [Formula: see text] correspond to the high-frequency discharge of sensory neurons and the need for longer-term prediction, respectively. Taking inspiration from the sensorimotor system, the U-expansion can potentially provide an analytical background for the development of algorithms designed for the fast and accurate feedback control of nonlinear systems.