Dynamic programming in problems of identifying distributed parameter systems

The problem of identifying the input of a system governed by a “semi-linear” evolution equation of parabolic type, based on the results of observations subject to undefined disturbances, is investigated. Estimates of the input, optimal in the sense of the so-called H ∞-criterion, are obtained. The i...

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Bibliographic Details
Published inJournal of applied mathematics and mechanics Vol. 62; no. 6; pp. 831 - 842
Main Authors Kurzhanskii, A.B., Sivergina, I.F.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 1998
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Summary:The problem of identifying the input of a system governed by a “semi-linear” evolution equation of parabolic type, based on the results of observations subject to undefined disturbances, is investigated. Estimates of the input, optimal in the sense of the so-called H ∞-criterion, are obtained. The information function of the system—the value function in an appropriate optimization problem—is evaluated. The relations between the information function and information sets are indicated. Optimality principles adequate to the proposed formulations of the problem are formulated and the corresponding dynamic programming equations are derived. Procedures for regularizing the problem, based on evolution equations of the input estimates, are proposed for the heat-conduction equation.
ISSN:0021-8928
DOI:10.1016/S0021-8928(98)00107-5