2020/01/17 by P. V. Shnurkov, Shnurkov, P. V.
Computer Science · Economics, Econometrics and Finance · Engineering · #93E20 #Aerospace Engineering and Control Systems #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2001.06424
openalex publication_date 2020/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a new method for solving the problem of optimal control of semi-Markov processes with finitely many states is considered. A new form of the assertion on an extremum of a liner-fractional integral functional given on a set of probability measures is formulated and proved. This form underlies the theorem of optimal control strategy for semi-Markov processes. It is proved that the solution of the optimal control problem for a semi-Markov process with finitely many states is completely determined by the extremum properties of the so-called test function of the liner-fractional integral functional which is the control quality index. At the same time, an explicit analytic representation was obtained for this test function in terms of the initial probability characteristics of the semi-Markov model.