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Infinite‐Dimensional Linear Systems: a Distributional Approach
Author(s) -
Opmeer Mark R.
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611505015315
Subject(s) - mathematics , resolvent , linear system , class (philosophy) , invariant (physics) , quadratic equation , linear control systems , pure mathematics , algebra over a field , mathematical analysis , computer science , geometry , artificial intelligence , mathematical physics
We introduce the concept of a distributional resolvent linear system and solve the linear quadratic optimal control problem for this class of systems. The class of distributional resolvent linear systems includes all linear time‐invariant systems that have been studied in the control literature. We show connections with integrated semigroups and distribution semigroups and we consider some examples of systems described by partial differential equations that could not be handled by the existing theory. 2000 Mathematics Subject Classification 47A48, 47D62, 49N10, 93C20.