Optimal control yields power law behavior

Abstract

Power law tails can be observed in the statistics of human motor control such as the balancing of a stick at the fingertip. We derive a simple control algorithm that employs optimal parameter estimation based on past observations. The resulting control system self-organizes into a critical regime, whereby the exponents of power law tails do not depend on system parameters. The occurrence of power laws is robust with respect to the introduction of delays and a variation in the length of the memory trace. Our results suggest that multiplicative noise causing scaling behavior may result from optimal control. © Springer-Verlag Berlin Heidelberg 2005.