Исследование предиктивных схем управления функционированием организационно-технических систем

Abstract

Organizational and technical systems are the most common tool for solving national economic problems. However, due to the personnel included in them, they are characterized by stochastic behavior, which raises the issue of developing their probabilistic model. On the other hand, the probabilistic apparatus is a tool for forecasting future phenomena and situations and therefore a mechanism for its use in predictive (forecast) management is needed. For this purpose, the work uses the first probabilistic approximation in the form of a Markov process and its description by the Fokker–Planck–Kolmogorov equation. The purpose of the study is to formulate and solve optimal control problems with probabilistic control quality criteria for a tracking predictive control scheme, as well as to develop a mechanism for metasystem switching of mo¬dels in the case of an adaptive scheme with a predictive model in the control loop. Materials and methods. Based on the analysis of scientific ideas and methodological approaches in predictive management of domestic and foreign authors, as well as mathematical methods and models, two schemes for implementing predictive management were selected to improve the efficiency of the functioning of organizational and technical systems: tracking schemes and adaptive management. Results. The optimal control problem was solved using two methods: Pontryagin's maximum principle and Bellman's principle of dynamic programming. It is shown that in the first case there is a convex upward strategy for achieving the target value of the controlled value with a maximizing approach, and in the second case the result is a convex downward strategy used for the optimal consumption of management resources. In addition, for another predictive control scheme – adaptive with a predictive model in the loop, the effectiveness of using the strategy of metasystem switching of models with the formulation and solution of six metasystem problems has been proven. Conclusion. The proposed approach can be used when designing management systems in organizational and technical systems and choosing behavior strategies in difficult market conditions when solving problems of their development.