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IMA Journal of Mathematical Control and Information 2001 18(3):405-425; doi:10.1093/imamci/18.3.405
© 2001 by Institute of Mathematics and its Applications
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Finite time linear quadratic control for weakly regular linear systems

Ming-Chu Gao1 and Jin-Chuan Hou1

1 Department of Mathematics, Shanxi Teachers' University, Linfen, Shanxi 041004, People's Republic of China. Email: mcgao@dns.sxtu.edu.cn

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.


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