Email this article On the Lagrange Duality of Stochastic and Deterministic Minimax Control and Filtering Problems
- Authors: Kogan M.M1
-
Affiliations:
- Nizhny Novgorod State University of Architecture and Civil Engineering
- Issue: No 2 (2023)
- Pages: 35-53
- Section: Articles
- URL: https://journals.rcsi.science/0005-2310/article/view/144255
- DOI: https://doi.org/10.31857/S0005231023020022
- EDN: https://elibrary.ru/OMHKZN
- ID: 144255
Cite item
Open Access
Access granted
Subscription Access
Abstract
As shown below, the linear operator norms in the deterministic and stochastic cases are optimal values of the Lagrange-dual problems. For linear time-varying systems on a finite horizon, the duality principle leads to stochastic interpretations of the generalized H2 and H∞ norms of the system. Stochastic minimax filtering and control problems with unknown covariance matrices of random factors are considered. Equations of generalized H∞-suboptimal controllers, filters, and identifiers are derived to achieve a trade-off between the error variance at the end of the observation interval and the sum of the error variances on the entire interval.
About the authors
M. M Kogan
Nizhny Novgorod State University of Architecture and Civil Engineering
Author for correspondence.
Email: mkogan@nngasu.ru
Nizhny Novgorod, Russia
References
- Куржанский А.Б. Управление и наблюдение в условиях неопределенности. М.: Наука, 1977.
- Квакернаак Х., Сиван Р. Линейные оптимальные системы управления. М.: Мир, 1977.
- Kailath T., Sayed A.H., Hassibi B. Linear Estimation. New Jersey: Prentice Hall, 2000.
- Hinrichsen D., Pritchard A.J. Stochastic H∞ // SIAM J. Control Optim. 1998. V. 36. No. 5. P. 1504-1538.
- Petersen I.R., Ugrinovskii V.A., Savkin A.V. Robust Control Design Using H∞- Methods. London: Springer-Verlag, 2000.
- Schweppe F.C. Recursive State Estimation: Unknown but Bounded Errors and System Inputs // IEEE Trans. Autom. Control. 1968. V. 13. No. 1. P. 22-28.
- Wilson D. Extended Optimality Properties of the Linear Quadratic Regulator and Stationary Kalman Filter // IEEE Trans. Autom. Control. 1990. V. 35. No. 5. P. 583-585.
- Willems J.C. Deterministic least squares filtering. Journal of Econometrics. 2004. V. 118. P. 341-373.
- Buchstaller D., Liu J., French M. The Deterministic Interpretation of the Kalman Filter // Int. J. Control. 2021. V. 94. No. 11. P. 3226-3236.
- Коган М.М. Оптимальные оценивание и фильтрация при неизвестных ковариа циях случайных факторов // АиТ. 2014. № 11. С. 88-109.
- Boyd S., Vandenberghe L. Convex Optimization. Cambridge: University Press, 2004.
- Черноусько Ф.Л. Оценивание фазового состояния динамических систем. М.: Наука, 1988.
- Wilson D.A. Convolution and Hankel Operator Norms for Linear Systems // IEEE Trans. Autom. Control. 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.
- Баландин Д.В., Коган М.М. Синтез законов управления на основе линейных матричных неравенств. М.: Физматлит, 2007.
- Hsieh C., Skelton R. All Covariance Controllers for Linear Discrete-Time Systems // IEEE Trans. Autom. Control. 1990. V. 35. No. 8. P. 908-915.
