How Can Brain Learn to Control a Nonholonomic System?

Abstract

Humans can often conduct both linear and nonlinear control tasks after a sufficient number of trials, even if they initially do not have sufficient knowledge about the system's dynamics and the way to control it. Theoretically, it is well known that some nonlinear systems cannot be stabilized asymptotically by any linear controllers and we have reported by an f-MRI experiment that different types of information may be involved in linear and nonlinear control tasks, respectively, from a brain function mapping point of view. In this paper, from a controllability analysis, we still show a possibility that human may use a linear control scheme for such nonlinear control tasks by switching the linear controllers with a virtual constraint. It is suggested that the proposed virtual constraint can play an important role to overcome a limitation of the linear controllers and to mimic human control behavior.