Email this article 
Suppressing Exogenous Disturbances in a Discrete-Time Control System as an Optimization Problem
- Authors: Khlebnikov M.V.1
-
Affiliations:
- Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
- Issue: No 10 (2023)
- Pages: 104-117
- Section: Topical issue
- URL: https://gynecology.orscience.ru/0005-2310/article/view/646727
- DOI: https://doi.org/10.31857/S0005231023100094
- EDN: https://elibrary.ru/YBXHZN
- ID: 646727
Cite item
Open Access
Access granted
Subscription or Fee Access
Abstract
This paper proposes a novel approach to suppressing bounded exogenous disturbances in a linear discrete-time control system by a static state- or output-feedback control law. The approach is based on reducing the original problem to a nonconvex matrix optimization problem with the gain matrix as one variable. The latter problem is solved by the gradient method; its convergence is theoretically
justified for several important special cases. An example is provided to demonstrate the effectiveness of the iterative procedure proposed.
About the authors
M. V. Khlebnikov
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
Author for correspondence.
Email: khlebnik@ipu.ru
Moscow, Russia
References
- Boyd S., El Ghaoui L., Feron E., Balakrishnan V. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
- Назин С.А., Поляк Б.Т., Топунов М.В. Подавление ограниченных внешних возмущений с помощью метода инвариантных эллипсоидов // АиТ. 2007. № 3. С. 106-125.
- Поляк Б.Т., Хлебников М.В., Щербаков П.С. Управление линейными системами при внешних возмущениях: Техника линейных матричных неравенств. М.: ЛЕНАНД, 2014.
- Kalman R.E. Contributions to the Theory of Optimal Control // Boletin de la Sociedad Matematica Mexicana. 1960. V. 5. No. 1. P. 102-119.
- Levine W., Athans M. On the Determination of the Optimal Constant Output Feedback Gains for Linear Multivariable Systems // IEEE Trans. Automat. Control. 1970. V. 15. No. 1. P. 44-48.
- Поляк Б.Т., Хлебников М.В. Синтез статического регулятора для подавления внешних возмущений как задача оптимизации // АиТ. 2021. № 9. С. 86-115.
- Хлебников М.В. Сравнение гарантирующего и калмановского фильтров // АиТ. 2023. № 4. С. 64-95.
- Поляк Б.Т. Введение в оптимизацию. 2-е изд. М.: УРСС, 2014.
Supplementary files
