A STRUCTURAL OBSERVATION ON PORT-HAMILTONIAN SYSTEMS

被引：1

作者：

Picard, Rainer H. ^{[1
]}

Trostorff, Sascha ^{[2
]}

Watson, Bruce ^{[3
]}

Waurick, Marcus ^{[4
]}

机构：

[1] Tech Univ Dresden, Dept Math, D-01062 Dresden, Saxony, Germany

[2] CAU Kiel, Math Seminar, D-24118 Kiel, Germany

[3] Univ Witwatersrand, Sch Math, ZA-2000 Johannesburg, South Africa

[4] TU Bergakademie Freiberg, D-09599 Freiberg, Germany

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2023年 / 61卷 / 02期

关键词：

port-Hamiltonian systems; m-accretive operators; congruences; BOUNDARY CONTROL-SYSTEMS; WELL-POSEDNESS; OPERATORS;

D O I：

10.1137/21M1441365

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study port-Hamiltonian systems on a family of intervals and characterize all boundary conditions leading to m-accretive realizations of the port-Hamiltonian operator and thus to generators of contractive semigroups. The proofs are based on a structural observation that the port-Hamiltonian operator can be transformed to the derivative on a familiy of reference intervals by suitable congruence relations, allowing for studying the simpler case of a transport equation. Moreover, we provide well-posedness results for associated control problems without assuming any additional regularity of the operators involved.

引用

页码：511 / 535

页数：25

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