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

Extended phase space description of human-controlled systems dynamics