Journal Article

Finite time linear quadratic control for weakly regular linear systems

Ming‐Chu Gao and Jin‐Chuan Hou

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 18, issue 3, pages 405-425
Published in print September 2001 | ISSN: 0265-0754
Published online September 2001 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/18.3.405
Finite time linear quadratic control for weakly regular linear systems

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This paper is devoted to the study of the finite time linear quadratic (LQ) control problem for weakly regular linear systems, a rather broad class of infinite dimensional linear systems with unbounded input and output operators. We show that the finite time LQ optimal control problem for weakly regular linear systems has a unique solution for every initial state. We give a formula for the optimal cost operator [prod ] (t) and show that {[prod ] (t)} is a strongly continuous family of bounded linear operators. Finally, we prove that, under certain conditions, the optimal cost operator satisfies a differential Riccati equation, as in the cases of classical bounded systems and of Pritchard–Salamon systems.

Keywords: weakly regular systems; finite time LQ control problem; Riccati equations

Journal Article.  0 words. 

Subjects: Mathematics

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