SYSTEM CONTROL IN A CONTINUOUS STOCHASTIC INPUT PROCESS
Abstract
In this article, a mathematical model of the control of a continuous stochastic production system is described. This system can also be a power supply system. An analytical model has been developed to
describe the influence of production and stock on hierarchical spatial pattern and demand. In production systems where the concept of inventories/stocks does not have a standard meaning in terms of
product storage, as in an energy system, they take on the role of supply of additional capacities that are optimally released according to demand. A system of differential equations describing the dynamics of a continuous system is solved using a Laplace transformation. Due to the stochastic nature of system inputs, the optimality criteria with the Wiener filter are satisfied. The Wiener-Hopf equation is solved by the spectral factorization method. The results of the presented mathematical model can be used as relevant information for the process of decision making in the operation of business systems,
including energy systems. The operation of a mathematical model and the analysis of the results is illustrated with two examples of different demand functions.
Downloads
References
M. Bogataj, J. Usenik: Fuzzy approach to the spatial games in the total market area. International journal of production economics, Vol. 93–94, pp. 493–503, 2005
D. Kovačič, J. Usenik, M. Bogataj: Optimal decisions on investments in urban energy cogeneration plants ‐ extended MRP and fuzzy approach to the stochastic systems. International journal of production economics, Vol. 183, part B, pp. 583‐595, 2017
E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, Inc., New York, 1999
C. Schneeweiss: Regelungstechnische stochastische Optimierung Verfahren in Unternehmensforschung und Wirtschsaftstheorie, Springer Verlag, Berlin, 1971
J. Usenik, M. Bogataj: A fuzzy set approach for a location‐inventory model. Transportation planning technology, Vol. 28, no. 6, pp. 447–464, 2005
J. Usenik, M. Vidiček, M. Vidiček, J. Usenik: Control of the logistics system using Laplace transforms and fuzzy logic. Logistics and sustainable transport, Vol. 1, issue 1, pp. 1‐19, 2008
J. Usenik: Mathematical model of the power supply system control. Journal of Energy Technology, Vol. 2, iss. 3, pp. 29‐46, 2009
J. Usenik, M. Repnik: System control in conditions of discrete stochastic input process. Journal of energy technology, Vol. 5, iss. 1, pp. 37‐53, 2012
J. Usenik: Differential equations, difference equations and fuzzy logic in control of dynamic systems. Journal of energy technology, Vol. 9, iss. 2, pp. 39‐54, 2016
Winston, W., L.: Operations research, Applications and Algorithms, Duxbury Press, Belmont, California, pp. 77
