This article is cited in 2 papers

Lower Bounds for the Rate of Convergence of Dynamic Reconstruction Algorithms for Distributed-Parameter Systems

E. V. Vasil'eva

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: We obtain lower bounds for the rate of convergence of reconstruction algorithms for distributed-parameter systems of parabolic type. In the case of a pointwise constraint on control for known reconstruction algorithms, we establish a lower bound on the rate of convergence, which shows that, given certain conditions, for each solution of the system one can choose such a collection of measurements so that the reconstruction error will not be less than a certain value. In the case of unbounded controls, we obtain lower bounds for a possible reconstruction error for each trajectory as well as for a given set of trajectories. For a system of special form, we construct an algorithm for which we obtain upper and lower bounds for accuracy having identical order for a specific choice of matching of the parameters.

UDC: 517.977

Received: 15.11.2003

DOI: 10.4213/mzm147

 English version: Mathematical Notes, 2004, 76:5, 628–639

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