The paper deals with the optimal positional control actions for linear discrete dynamic stationary objects. Methods of the real-time constructing of the implementations of optimal feedbacks are described based on reduction of the sequence of optimal programs to linear programming problems (LP).To solve the problem the duel method of LP with a long steps is used to correct supports, the parallelizing and acceleration of computations with the recurrent equation and methods of "set of weight" are applied. A real-time observation problem at uncertainty in initial states is considered to the linear dynamic object with discrete measurement devices which is reduced to the series of LP problems. Both of the problems are solved by the dual method of LP. To accelerate the computations of control actions it is suggested to use the parallelizing procedure.

Rafail Gabasov, Dr. Sci. (Phys.–Math.), Prof., Belarus State University, 4, Nezavisimost avenue, Minsk, 220050, Republic of Belarus, e-mail: kirillova.f@yandex.ru

Faina Kirillova, Corresponding-member of National Academy of Science of Belarus, Dr. Sci. (Phys.–Math.), Prof., Principal Investigator, Institute of mathematics NASB, 11, Surganov st., Minsk, 200072, Republic of Belarus, e-mail: kirillova.f@yandex.ru

Gabasov R., Kirillova F.M. Some Aspects of Real-time Control of Linear Stationary Dynamic Systems. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 27, pp. 15-27. (In Russian) https://doi.org/10.26516/1997-7670.2019.27.15

1. Gabasov R., Kirillova F.M. and Tyatyushkin A. I. Constructive optimization techniques. Vol. 1. Linear Problems. Minsk, BGU Publishing House, 1984. (in Russian).
2. Gabasov R., Kirillova F.M., Paulianok N.S. Optimal control of  a dynamic system using perfect measurements of its states. Doklady Mathematics, 2012, no. 3, pp. 436–440. https://doi.org/10.1134/S1064562412030209
3. Gabasov R., Kirillova F.M., Vo Thi Tan Ha. Optimal real-time control of multidemensional dynamic plant. Automation and Remote Control, 2015, no. 1(85), pp. 121–135. https://doi.org/10.1134/S0005117915010099
4. Gabasov R., Kirillova F.M., Poyasok E.I. Real-time optimal observation of a linear dynamic system. Doklady Mathematics, 2013, vol. 87, issue 1, pp. 120–123. https://doi.org/10.1134/S1064562413010080
5. Gabasov R., Kirillova F.M. Real-time control of a dynamic object under conditions of constantly acting disturbances. Doklady NAN of Belarus, 2017, no. 6, pp. 7–12. (in Russian)
6. Fedorenko R.P. Approximate solution of optimal control problems. Moscow, 1978, 486 p.
7. Gabasov R., Kirillova F.M., Poyasok E.I. Robust optimal control on imperfect measurement of dynamic systems states. Appl. Comput. Math, 2009, no. 1, pp. 54–69.