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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Rasina I. V.
,
Guseva I. S.
,
Fesko O. V.
,
Usenko O. V.
Method of control local improvement for non-homogeneous discrete systems // BSU bulletin. Mathematics, Informatics. - 2016. №1. . - С. 27-37.
Title:
Method of control local improvement for non-homogeneous discrete systems
Financing:
Codes:
DOI: 10.18101/2304-5728-2016-1-27-37UDK: 517.977
Annotation:
In studying of non-homogeneous control systems by different schools the main attention is paid to continuous systems with time-varying structure. The necessary and sufficient conditions, as well as iterative procedures have been obtained for them. One of the approaches is to generalize the sufficient conditions for optimality of Krotov type on such systems. On this basis a non- homogeneous hierarchical model of controlled structure have been developed in which the lower level is a description of similar processes at different stages,and the upper level connects these descriptions into a single process, and controls the functioning of the system in whole. In various control problems, in particular in optimization problems, both levels are considered in interaction.
We have considered the class of non-homogeneous discrete systems for which both levels are discrete. These systems are prevalent in practice and can be obtained from the process of continuous systems digitalization for solution of optimization problems using iterative methods. We have formulated the suf- ficient conditions of optimality of Krotov type for this class of systems. These conditions and the principle of localization are used to construct improvement method. The article contains illustrative examples.
Keywords:
optimal control, discrete systems, approximate methods of control improvement.
List of references:
1. Propoi A. I. O printsipe maksimuma dlya diskretnykh sistem upravleniya About Maximum Principle for Discrete Control Systems]. Avtomatika i tele- mekhanika – Automation and Telecontrol. 1965. V. 26. No. 7. Pp. 1177–1187.

2. Propoi A. I. Elementy teorii optimal'nykh diskretnykh protsessov [Ele- ments of the Theory of Optimal Discrete Processes]. Moscow: Nauka Publ., 1973. 256 p.

3. Boltyanskii V. G. Optimal'noe upravlenie diskretnymi sistemami [Op- timal Control of Discrete Systems]. Moscow: Nauka Publ., 1973. 448 p.

4. Evtushenko Yu. G. Metody resheniya ekstremal'nykh zadach i ikh primenenie v sistemakh optimizatsii [Methods for Solving Extreme Problems and Their Use in Optimization Systems]. Moscow: Nauka Publ., 1982. 432 p.

5. Gorbunov V. K. O svedenii zadach optimal'nogo upravleniya k ko- nechnomernym [Reduction of Optimal Control Problems for Finite- Dimensional Ones]. Zhurnal vychislitel’noi matematiki i matematicheskoi fiziki–Journal of Mathematics and Mathematical Physics. 1978. V. 18. No. 5. Pp. 1083–1095.

6. Gurman V. I. K teorii optimal'nykh diskretnykh protsessov [To the Theory of Optimal Discrete Processes]. Avtomatika i telemekhanika – Automa- tion and Telecontrol. 1973. No. 6. Pp. 53–58.

7. Vasil'ev S. N. Teoriya i primenenie logiko-upravlyaemykh sistem [Theory and Application of Logic-Control Systems]. Identifikatsiya sistem i zadachi upravleniya – System Identification and Control Problems (SICPRO'03). Proc. 2nd Int. Conf. (SICPRO'03). 2003. Pp. 23–52.

8. Bortakovskii A. S. Dostatochnye usloviya optimal'nosti upravleniya determinirovannymi logiko-dinamicheskimi sistemami [The Sufficient Conditions for Optimal Control of Deterministic Logic-Dynamic Systems]. Informatika. V. 2–3. Ser. Avtomatizatsiya proektirovaniya – Computer Science. V. 2–3. Ser. Design Automation. 1992. Pp. 72–79.

9. Miller B. M., Rubinovich E. Ya. Optimizatsiya dinamicheskikh sistem s impul'snymi upravleniyami [Optimization of Dynamical Systems with Impulse Controls]. Moscow: Nauka Publ., 2005.

10. Lygeros J. Lecture Notes on Hybrid Systems. Cambridge: University of Cambridge, 2003.

11. Krotov V. F., Gurman V. I. Metody i zadachi optimal'nogo upravleniya [Methods and Problems of Optimal Control]. Moscow: Nauka Publ., 1973. 448 p.

12. Krotov V. F. Dostatochnye usloviya optimal'nosti dlya diskretnykh upravlyaemykh sistem [The Sufficient Conditions of Optimality for Discrete Control Systems]. Doklady Akademii nauk SSSR – Reports of the USSR Acad- emy of Sciences. 1967. V. 172. No. 1. Pp. 18–21.

13. Gurman V. I., Rasina I. V. Diskretno-nepreryvnye predstavleniya impul'snykh reshenii upravlyaemykh sistem [Discrete-Continuous Presentation of Impulse Solutions]. Avtomatika i telemekhanika – Automation and Telecontrol. 2012. No. 8. Pp. 16–29.

14. Rasina I. V. Ierarkhicheskie modeli upravleniya sistemami neodnorodnoi struktury [Hierarchical Control Models of Systems Having Inhomogeneous Structure]. Moscow: Fizmatlit Publ., 2014.

15. Gurman V. I., Rasina I. V. O prakticheskikh prilozheniyakh dostatoch- nykh uslovii sil'nogo otnositel'nogo minimuma [About Practical Applications of the Sufficient Conditions for Strong Relative Minimum]. Avtomatika i telemekhanika – Automation and Telecontrol. 1979. No. 10. Pp. 12–18.