SYSTEM CONTROL IN A CONTINUOUS STOCHASTIC INPUT PROCESS - Usenik, Janez (Journal of Energy Technology, 2024)
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 todescribe 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 ofproduct 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.