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 H$_{2}$ and H$_{\infty}$ norms of the system. Stochastic minimax filtering and control problems with unknown covariance matrices of random factors are considered. Equations of generalized H$_{\infty}$-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.
Keywords:stochastic minimax control, Kalman filter, Lagrange duality, generalized H$_{\infty}$-optimal control and filtering, generalized H$_{2}$-optimal control, linear matrix inequalities.
Presented by the member of Editorial Board:B. M. Miller
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