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

References:

1. Malakhov A.N. Kumulyantnyy analiz sluchaynykh negaussovykh protsessov i ikh preobrazovaniy (Cumulative Analysis of Random Non-Gaussian Processes and Their Transformations), Moscow, 1978. (in Russ.)
2. Zhang Y., Yang Y., Shi P., Pan J.-S. International Journal of Systems Science, 2018, no. 16(49),  pp. 3296–3306.
3. Zeng Y., Zhu W.Q. Solid Mechanics and its Applications, 2011, vol. 29, рp. 147–155.
4. Levkina S.V. Journal of Instrument Engineering, 2017, no. 2(60), pp. 132–135.
5. Vodovozov A.M. Measurement Techniques, 2018, no. 9(61), pp. 950–954.
6. Zhou W., Zhang R., Zhou Y. Computers and Industrial Engineering, 2013, no. 4(66), pp. 643–652. 
7. Panteleev A.V., Rybakov K.A. Automation and remote control, 2011, no. 2(72), pp. 393–404.
8. Rashid R., Hoseini S.F., Gholamian M.R., Feizabadi M. Journal of Industrial Engineering International, 2015, no. 4(11), pp. 485–494.
9. Yongjun Du, Shubin Si, Tongdan Jin. IEEE Transactions on Reliability, 2019, no. 1(68), pp. 267–279.
10. Vodovozov A.M. Journal of Instrument Engineering, 2018, no. 6(61), pp. 485–489.
11. Sobolev V.I. Measurement Techniques, 2014, no. 3(57), pp. 247–254.
12. Vodovozov A.M. Measurement Techniques, 2018, no. 2(61), pp. 177–181.
13. Kingman J. Poisson Processes, Oxford University Press, 1992. 
14. Shynk J.J. Mathematical Foundations for Linear Circuits and Systems in Engineering, Santa Barbara, University of California, 2016, 656 p.
15.  Radi B., El Hami A. Advanced Numerical Methods with Matlab: Function Approximation and System Resolution, Hoboken, Wiley, 2018.
16. Thanki R.M., Kothari A.M. Digital image processing using SCILAB, NY, Springer International Publishing, 2018.