Asymptotic Semantization of Data in Control Systems

Abstract

Asymptotic methods for analyzing large deviations in this work are used to convert information about the state of a controlled diffusion process into probabilistic estimates of the normal or abnormal development of the process. Thus, over the reflex contour of local stabilization a system of global semantic control is implemented, a kind of second signal system. A functional analytical approach similar to the weak convergence of probabilistic measures is used as an analysis tool, which makes it possible to significantly expand the conditions for applying the method. Global control is reduced to solving the Lagrange problem in the form of Pontryagin for the system of ordinary differential equations (system of paths), the Ventzel-Freidlin action functional (or "rate function" in some English literature), which is presented here as an integral-quadratic criterion for control functions in the system of paths, and the boundary condition in the form of the critical state of the system. A bounded solution of the Lagrange — Pontryagin problem on the half-line, which gives a prototype of the quasipotential of the system of paths, is called the A-profile of the critical state. The A-profile makes it possible to significantly simplify the procedure for analyzing large deviations, up to its implementation in real time and the implementation of the global control loop (2nd signaling system). The resulting two-tier architecture is positioned as a baseline to achieve the functional stability of the control system. It is speculated that this role of the apparatus of large deviations takes place in biological evolving systems, including the formation of languages and other attributes of the evolution of higher human nervous activity.