On the Lagrange Duality of Stochastic and Deterministic Minimax Control and Filtering Problems

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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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