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Regular version of the site

Article

Optimal Control Problem in a Stochastic Model with Periodic Hits on the Boundary of a Given Subset of the State Set (Tuning Problem)

P. V. Shnurkov.

In this paper, a general stochastic model with controls applied at the moments
when the random process hits the boundary of a given subset of the state set is
proposed and studied. The general concept of the model is formulated and its
possible applications in technical and economic systems are described. Two versions
of the general stochastic model, the version based on the use of a continuous-time
semi-Markov process with embedded absorbing Markov chain and the version based
on the use of a discrete-time Markov process with absorbing states, are analyzed.
New representations of the stationary cost index of the control quality are obtained
for both versions. It is shown that this index can be represented as a linear-fractional
integral functional of two discrete probability distributions determining the control
strategy. The results obtained by the author of this paper about an extremum
of such functionals were used to prove that, in both versions of the model, the
control is deterministic and is determined by the extremum points of functions of
two discrete arguments for which the explicit analytic representations are obtained.
The perspectives of the further development of this stochastic model are outlined.