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Design of Suboptimal Robust Controllers Based on a Priori and Experimental Data
- Authors: Kogan M.M.1, Stepanov A.V.1
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Affiliations:
- Nizhny Novgorod State University of Architecture and Civil Engineering
- Issue: No 8 (2023)
- Pages: 24-42
- Section: Linear systems
- URL: https://journals.rcsi.science/0005-2310/article/view/142059
- DOI: https://doi.org/10.31857/S0005231023080020
- EDN: https://elibrary.ru/HAQKRE
- ID: 142059
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Abstract
This paper develops a novel unified approach to designing suboptimal robust control laws for uncertain objects with different criteria based on a priori information and experimental data. The guaranteed estimates of the γ0, generalized H2, and H∞ norms of a closed loop system and the corresponding suboptimal robust control laws are expressed in terms of solutions of linear matrix inequalities considering a priori knowledge and object modeling data. A numerical example demonstrates the improved quality of control systems when a priori and experimental data are used together.
About the authors
M. M. Kogan
Nizhny Novgorod State University of Architecture and Civil Engineering
Email: mkogan@nngasu.ru
Nizhny Novgorod, Russia
A. V. Stepanov
Nizhny Novgorod State University of Architecture and Civil Engineering
Author for correspondence.
Email: andrey8st@yahoo.com
Nizhny Novgorod, Russia
References
- Поляк Б.Т., Щербаков П.С. Робастная устойчивость и управление. М.: Наука, 2002.
- Petersen I.R., Tempo R. Robust Control of Uncertain Systems: Classical Results and Recent Developments // Automatica. 2014. V. 50. No. 5. P. 1315-1335.
- Андриевский Б.Р., Фрадков А.Л. Метод скоростного градиента и его приложения // АиТ. 2021. № 9. С. 3-72.
- Annaswamy A.A., Fradkov A.L. A Historical Perspective of Adaptive Control and Learning // Annual Reviews in Control. 2021. V. 52. P. 18-41.
- De Persis C., Tesi P. Formulas for Data-Driven Control: Stabilization, Optimality and Robustness // IEEE Trans. Automat. Control. 2020. V. 65. No. 3. P. 909-924.
- Waarde H.J., Eising J., Trentelman H.L., Camlibel M.K. Data Informativity: a New Perspective on Data-Driven Analysis and Control // IEEE Trans. Automat. Control. 2020. V. 65. No. 11. P. 4753-4768.
- Berberich J., Koch A., Scherer C.W., Allgower F. Robust data-driven state-feedback design // Proc. Amer. Control Conf. 2020. P. 1532-1538.
- Waarde H.J., Camlibel M.K., Mesbahi M. From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma // IEEE Trans. Automat. Control. 2022. V. 67. No. 1. P. 162-175.
- Biso A., De Persis C., Tesi P. Data-driven Control via Petersen's Lemma // Automatica. 2022. V. 145. Article 110537.
- Willems J.C., Rapisarda P., Markovsky I., De Moor B. A note on persistency of excitation // Syst. Control Lett. 2005. V. 54. P. 325-329.
- Якубович В.А. S-процедура в нелинейной теории управления // Вестник Ленинградского университета. Математика. 1977. Т. 4. С. 73-93.
- Petersen I.R. A stabilization algorithm for a class of uncertain linear systems // Syst. Control Lett. 1987. V. 8. P. 351-357.
- Doyle J.C. Analysis of feedback systems with structured uncertainties // IEE Proc. 1982. V. 129. Part D(6). P. 242-250.
- Safonov M.G. Stability margins of diagonally perturbed multivariable feedback systems // IEE Proc. 1982. V. 129. Part D(6). P. 251-256.
- Kogan M.M. Optimal discrete-time H∞/γ0 ltering and control under unknown covariances // Int. J. Control. 2016. V. 89. No. 4. P. 691-700.
- Wilson D.A. Convolution and Hankel Operator Norms for Linear Systems // IEEE Trans. Autom. Control. 1989. V. 34. No. 1. P. 94-97.
- Баландин Д.В., Бирюков Р.С., Коган М.М. Минимаксное управление уклонениями выходов линейной дискретной нестационарной системы // АиТ. 2019. № 12. С. 3-24.
- Boyd S., Vandenberghe L. Convex Optimization. Cambridge: University Press, 2004.
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