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Об аналитической структуре некоторых видов целевых функционалов, связанных с задачами управления полумарковскими случайными процессами
Информатика и ее применения. 2022. Т. 16. № 2. С. 75–84.
Shnourkoff P. V.
The present author investigates the analytical structure of three kinds of functionals from a controllable semi-Markov process with a finite set of states. It is proved that all these mathematical objects can be represented in the form of a fractional-linear integral functional defined on a finite set of probability measures that determine the control strategy of the corresponding semi-Markov process. For each of these functionals, explicit representations for the integrand functions of the numerator and denominator through the initial probabilistic characteristics of the controlled semi-Markov process are obtained. This result allows one to reduce the problem of optimal control of a semi-Markov process with a particular target functional to the problem of investigation on the global extremum of a given function of a finite number of variables.
Keywords: дробно-линейный интегральный функционалoptimal control of semi-Markovian processesbasic function of partial-linear integral functionalstochastic control modelspartial-linear integral functionalстохастические модели управленияоптимальное управление полумарковскими процессамиосновная функция дробно-линейного интегрального функционала
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