Article collection "Mathematical Problems of Cybernetics" №7, Moscow, 1998

Authors:Fedotkin M.A.

A nonlocal method for defining controlled random processes

Abstract:

Traditional methods of probabilistic model construction for statistically stable experiments with control come from a well-known approach which is used successfully in classical problems of automatic control. At the basis of the approach there's the general notion of measurable state spaces for the control system and the object of control. It allows defining a certain controlled random process by means of a family of conditional probability distributions for the control system measurer and for the object of control measures. In this case the constructed random process is not a mathematical model of a statistically stable experiment with control. One may say only that a problem about constructing a probabilistic model for the collective functioning of the control system and the object of control in time gets solved.
In this work we propose to view a statistically stable experiment with control from the standpoint of a general notion of a control system after Lyapunov, Yablonsky and Buslenko. Effective methods of nonlocal definition and methods for study of controlled random processes have been developing in this work taking into account the concrete nature and operation goals of evolutionary statistically stable experiments with control. To demonstrate the effectiveness of the proposed approach several problems in control of conflicting flows of nonhomogeneous customers have been solved. In particular, the flows of customers are formed in a random environment.

Keywords:

probability space, evolutionary experiment, Lyapunov – Yablonsky control system, simulation modeling