Riccati equations for stable well-posed linear systems: The generic case

被引：10

作者：

Curtain, RF ^{[1
]}

机构：

[1] Univ Groningen, Dept Math, NL-9700 AV Groningen, Netherlands

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2003年 / 42卷 / 05期

关键词：

Riccati equations; well-posed linear systems; weakly regular linear systems; Popov function; spectral factorizations; optimal control;

D O I：

10.1137/S0363012901399362

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Under the generic assumption that zero is in the resolvent set of the generator, we show that the optimal control problem for a stable well-posed linear system is equivalent to a control problem for its reciprocal system which has bounded generating operators. Consequently, the operator X that defines the optimal cost satisfies a Riccati equation with bounded operators. Previous results needed various regularity assumptions to obtain X as a solution to a Riccati equation resembling that in the finite-dimensional theory.

引用

页码：1681 / 1702

页数：22

共 50 条

[1] New Riccati equations for well-posed linear systems
Opmeer, MR
Curtain, RF
[J]. SYSTEMS & CONTROL LETTERS, 2004, 52 (05) : 339 - 347
[2] Quadratic optimal control of stable well-posed linear systems
Staffans, OJ
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (09) : 3679 - 3715
[3] Classes of well-posed linear systems
[J]. HANKEL NORM APPROXIMATION FOR INFINITE-DIMENSIONAL SYSTEMS, 2002, 277 : 13 - 62
[4] A well-posed setting of the problem of solving systems of linear algebraic equations
Tyrtyshnikov, E. E.
[J]. SBORNIK MATHEMATICS, 2022, 213 (10) : 1436 - 1443
[5] GEOMETRICAL WELL-POSED SYSTEMS FOR THE EINSTEIN EQUATIONS
CHOQUETBRUHAT, Y
YORK, JW
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1995, 321 (08): : 1089 - 1095
[6] Coprime factorizations and well-posed linear systems
Staffans, OJ
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1998, 36 (04) : 1268 - 1292
[7] Coprime factorizations and well-posed linear systems
Staffans, OJ
[J]. PROCEEDINGS OF THE 37TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, 1998, : 2751 - 2756
[8] Quadratic optimal control of well-posed linear systems
Staffans, OJ
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1998, 37 (01) : 131 - 164
[9] Hankel norm approximation for well-posed linear systems
Curtain, RF
Sasane, AJ
[J]. SYSTEMS & CONTROL LETTERS, 2003, 48 (05) : 407 - 414
[10] A semigroup characterization of well-posed linear control systems
Miriam Bombieri
Klaus-Jochen Engel
[J]. Semigroup Forum, 2014, 88 : 366 - 396

← 1 2 3 4 5 →