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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: Linear systems
- URL: https://rjmseer.com/0005-2310/article/view/646793
- DOI: https://doi.org/10.31857/S0005231023020022
- EDN: https://elibrary.ru/OMHKZN
- ID: 646793
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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
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