DOI 10.17586/0021-3454-2020-63-6-501-506

DOI 10.17586/0021-3454-2020-63-6-501-506

**UDC 681.514**

## NONLINEAR REAL-TIME PROBLEMS IN STOCHASTIC SYSTEM WITH POISSON COMPONENT

Vologda State University, Department of Control and Computer Systems; Professor, Head of the Department

**Abstract.**Nonlinear stochastic systems under pulsed input effects forming Poisson flows of events are considered. The process of nonlinear transformation in the system of information represented by time intervals between events is analyzed, and a given nonlinear functional in the Poisson flow intensity function is synthesized. The research is based on the probabilistic time-pulse representation of the Poisson process; the time interval between input events is used as an argument for calculations. An analytical solution to the problem accounting for the exponential distribution of random time intervals characteristic for the simplest Poisson flow is proposed. The algorithm of synthesis of a generalized nonlinear functional given as a table is considered, and formulas for calculating the original function are presented for the case when table data are approximated by power series with negative exponents. The results are confirmed by digital modeling in the Scilab package of applied mathematical programs. The proposed algorithm for configuring a computing device to reproduce a given analytically nonlinear functional can be applied for solution of practical problems in stochastic systems with a Poisson input signal, such as devices using ionizing radiation, queuing systems, etc.

**Keywords:**stochastic system, Poisson flow, time-pulse transformation, nonlinear functional, synthesis algorithm

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