The ADAR Method and Theory of Optimal Control in the Problems of Synthesis of Nonlinear Control Systems
https://doi.org/10.17587/mau.17.657-669
Abstract
In the paper the authors compare the known method of Analytical Design of the Aggregated Regulators (ADAR) with the method of Analytical Design of the Optimal Regulators (ADOR). The ADAR method has significant advantages: (i) easier procedure of analytical design of the nonlinear laws of the optimal control; (ii) physically clear presentation of the weight factors of the optimality criterions; and (iii) stability of the closed-loop optimal system. As opposed to the method of the optimal control, the ADAR method is free from the demand to solve Riccati's equation and Bellman's equation, and the procedure of the control laws' analytical design is easier. The control laws designed with ADAR method also may ensure sub-optimal transients in a system: time optimal and energy optimal in the mode of big deviations from the desired final state, as well as optimal to the #uadratic criterion of the generalized work (criterion of A. A. Krasovskii) in the mode of small deviations. The provided numerical eXamples display e#uivalency of these methods, as well as a significant difference in the approaches used for the analytical design of the control laws, i.e. in contrast to ADOR, in the ADAR method the optimizing functional is a constructed performance criteria, the structure and the parameters of which are defined by the designer of the control system in accordance with the object's physical properties and the desired engineering re#uirements.
About the Authors
A. A. Kolesnikov
Southern Federal University, Institute of Computer Technologies and Information Security
Russian Federation
Russian Federation
Al. A. Kolesnikov
Southern Federal University, Institute of Computer Technologies and Information Security
Russian Federation
Russian Federation
A. A. Kuz'menko
Southern Federal University, Institute of Computer Technologies and Information Security
Russian Federation
Russian Federation
References
1. Красовский А. А. Системы автоматического управления полетом и их аналитическое конструирование. М.: Наука, 1973. 560 с.
2. Seron M. M., Braslavsky J. H., Kokotovic P. V., Mayne D. Q. Feedback limitations in nonlinear systems: from Bode integrals to cheap control // IEEE Transactions on Automatic Control. 1999. Vol. 44, Iss. 4. P. 829-833.
3. Garcia C., Prett M. Model predictive control: theory and practice // Automatica. 1989. Vol. 25, Iss. 3. P. 335-348.
4. Astrom K. J., Kumar P. R. Control: A perspective // Automa-tica. 2014. Vol. 50, Iss. 1. P. 3-43.
5. Isidori A. Nonlinear control systems an introduction. Berlin: Springer-Verlag, 1995. 545 p.
6. Hull D. G. Optimal Control Theory for Applications. New York: Springer-Verlag, 2003. 384 p.
7. Burghes D., Graham A. Control and Optimal Control Theories with Applications. London: Woodhead Publishing, 2004. 400 p.
8. Филимонов Н. Б. Непостижимая эффективность математики и кризис современной теории управления // Тр. 4-го Меж-дунар. науч.-техн. семинара "Современные проблемы прикладной математики, информатики, автоматизации, управления". Севастополь: Изд-во ИПИ РАН, 2014. С. 16-28.
9. Филимонов Н. Б. Проблема качества процессов управления: смена оптимизационной парадигмы // Мехатроника, автоматизация, управление. 2010. № 12. С. 2-11. u
10. Современная прикладная теория управления: Ч. II. Сине-ргетический подход в теории управления / Под ред. А. А. Колесникова. Таганрог: Изд-во ТРТУ, 2000. 559 с.
11. Колесников А. А. Синергетическая теория управления. М.: Энергоатомиздат, 1994. 344 с.
12. Kolesnikov A. A. Introduction of synergetic control // Proc. of the American Control Conference ACC-2014, Portland, OR, USA, 4-6 June 2014. P. 3013-3016.
13. Буков В. Н., Сизых В. Н. Приближенный синтез оптимального управления в вырожденной задаче аналитического конструирования регуляторов // Автоматика и телемеханика. 1999. № 12. С. 16-32.
14. Летов А. М. Синтез оптимальных систем // Тр. II Меж-дунар. конгресса ИФАК "Оптимальные системы. Статистические методы". М.: Наука, 1965. 456 с.
15. Красовский А. А. Статистическая теория переходных процессов в системах управления. М.: Наука, 1968. 240 с.
16. This work was supported by RFBR (grant № 14-08-00782-a)
17. This work was supported by RFBR (grant № 14-08-00782-a)
Review
For citations:
Kolesnikov A.A., Kolesnikov A.A., Kuz'menko A.A. The ADAR Method and Theory of Optimal Control in the Problems of Synthesis of Nonlinear Control Systems. Mekhatronika, Avtomatizatsiya, Upravlenie. 2016;17(10):657-669. (In Russ.) https://doi.org/10.17587/mau.17.657-669
Views:
1373
.png)
Email this article 