CONVERGENCE OF ITERATION PROCESSES IN THE MODEL OF RESERVOIR CASCADE // BSU bulletin. Mathematics, Informatics. - 2019. №4. . - С. 31-39.

CONVERGENCE OF ITERATION PROCESSES IN THE MODEL OF RESERVOIR CASCADE

The article deals with the mathematical model of reservoirs, which allows studying various cascade control rules. One of the unresolved problems of using such models is the inequality of water volumes in reservoirs at the initial and final moments of the period of time, during which different control rules are compared. We have proposed an iterative algorithm for searching such initial volumes of water in reservoirs, which for a given control rule lead to coinciding volumes of water at the final moment. The convergence of this algorithm is shown.

dynamic system; simulation modelling; simple-iteration method; fixed point; reservoir cascade; control rules.

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Lotov A. V., Ryabikov A. I. Mnogokriterialnyi sintez optimalnogo upravleniya i ego primenenie pri postroenii pravil upravleniya kaskadom gidroelektrostantsii [Mul- ticriterial Synthesis of Optimal Control and Its Application in Constructing Control Rules for a Cascade of Hydroelectric Stations]. Proceedings of the Steklov Institute of Mathematics. 2014. Vol. 20, No. 4. Pp. 187–203.

Bolgov M. V., Sarmanov I. O., Sarmanov O. V. Markovskiye protsessy v gidrologii [Markov Chain in Hydrology]. Moscow: Institute of Water Problems RAS, 2009. 210 p.

Lotov A. V., Ryabikov A. I. Mnogokriterialnyi sintez optimalnogo upravleniya i ego primenenie pri postroenii pravil upravleniya kaskadom gidroelektrostantsii [Mul- ticriterial Synthesis of Optimal Control and Its Application in Constructing Control Rules for a Cascade of Hydroelectric Stations]. Proceedings of the Steklov Institute of Mathematics. 2014. Vol. 20, No. 4. Pp. 187–203.

Bolgov M. V., Sarmanov I. O., Sarmanov O. V. Markovskiye protsessy v gidrologii [Markov Chain in Hydrology]. Moscow: Institute of Water Problems RAS, 2009. 210 p.