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A solution to the problem of (A,B)-invariance for series

✍ Scribed by Ines Klimann

Book ID
104325443
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
260 KB
Volume
293
Category
Article
ISSN
0304-3975

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✦ Synopsis

The aim of this article is to study a standard problem of control theory, the (A; B)-invariance problem, which amounts to computing a maximal element X subject to conditions of the form AX 6 X + B and X 6 K. We give a solution to the problem in the framework of formal series over particular complete idempotent semirings. Over ΓΏnite idempotent semirings, we show that, under the assumption that B and K are recognizable series, the maximal solution exists and is also recognizable. We obtain a similar result for the inΓΏnite tropical semiring, with additional hypothesis that the series A is a language, but the notion of recognizable series has to be extended to the weaker notion of pseudo-recognizable series.

πŸ“œ SIMILAR VOLUMES

A solution to the problem of invariants
A solution to the problem of invariants for parabolic equations
✍ N.H. Ibragimov; S.V. Meleshko πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 206 KB

The article is devoted to the solution of the invariants problem for the one-dimensional parabolic equations written in the two-coefficient canonical form used recently by N.H. Ibragimov: A simple invariant condition is obtained for determining all equations that are reducible to the heat equation