  Humans are often incapable of precisely identifying and implementing the
desired control strategy in controlling unstable dynamical systems. That is,
the operator of a dynamical system treats the current control effort as
acceptable even if it deviates slightly from the desired value, and starts
correcting the actions only when the deviation has become evident. We argue
that the standard Newtonian approach does not allow to model such behavior.
Instead, the physical phase space of a controlled system should be extended
with an independent phase variable characterizing the operator motivated
actions. The proposed approach is illustrated via a simple non-Newtonian model
capturing the operators fuzzy perception of their own actions. The properties
of the model are investigated analytically and numerically; the results confirm
that the extended phase space may aid in capturing the intricate dynamical
properties of human-controlled systems.
