Using System Theory and Energy Methods to Prove Existence of Non-linear PDE's

Heiko J. Zwart

doi:10.1016/j.ifacol.2015.10.246

Using System Theory and Energy Methods to Prove Existence of Non-linear PDE's

Heiko J. Zwart

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Consider a network with linear dynamics on the edges, and observation and control in the nodes. Assume that on the edges there is no damping, and so the dynamics can be described by an infinite-dimensional, port-Hamiltonian system. For general infinite-dimensional systems, the zero dynamics can be difficult to characterize and are sometimes ill-posed. However, for this class of systems the zero dynamics are shown to be well-defined. Using the underlying structure, simple characterizations and a constructive procedure can be obtained.

Original language	Undefined
Title of host publication	5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015
Publisher	IFAC Proceedings
Pages	241-243
Number of pages	3
ISBN (Print)	2405-8963
DOIs	https://doi.org/10.1016/j.ifacol.2015.10.246
Publication status	Published - 2015
Event	5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015 - Lyon, France Duration: 6 Jul 2015 → 7 Jul 2015 Conference number: 5

Publication series

Name
Publisher	IFAC Proceedings
Number	13
Volume	48
ISSN (Print)	2405-8963

Workshop

Workshop	5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015
Abbreviated title	LHMNC
Country/Territory	France
City	Lyon
Period	6/07/15 → 7/07/15

Keywords

coupled wave equations
EWI-26572
zero dynamics
Port-Hamiltonian system
METIS-315602
Distributed-parameter systems
IR-99328
Boundary control
Networks

Access to Document

10.1016/j.ifacol.2015.10.246

http://eprints.eemcs.utwente.nl/secure2/26572/01/Zw-IFAC-15.pdf

Cite this

@inproceedings{9d4c6d697b5a49548e2a968268509d4a,

title = "Using System Theory and Energy Methods to Prove Existence of Non-linear PDE's",

abstract = "Consider a network with linear dynamics on the edges, and observation and control in the nodes. Assume that on the edges there is no damping, and so the dynamics can be described by an infinite-dimensional, port-Hamiltonian system. For general infinite-dimensional systems, the zero dynamics can be difficult to characterize and are sometimes ill-posed. However, for this class of systems the zero dynamics are shown to be well-defined. Using the underlying structure, simple characterizations and a constructive procedure can be obtained.",

keywords = "coupled wave equations, EWI-26572, zero dynamics, Port-Hamiltonian system, METIS-315602, Distributed-parameter systems, IR-99328, Boundary control, Networks",

author = "Zwart, {Heiko J.}",

note = "10.1016/j.ifacol.2015.10.246 ; 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015 ; Conference date: 06-07-2015 Through 07-07-2015",

year = "2015",

doi = "10.1016/j.ifacol.2015.10.246",

language = "Undefined",

isbn = "2405-8963",

publisher = "IFAC Proceedings",

number = "13",

pages = "241--243",

booktitle = "5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015",

}

Zwart, HJ 2015, Using System Theory and Energy Methods to Prove Existence of Non-linear PDE's. in 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015. IFAC Proceedings, pp. 241-243, 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015, Lyon, France, 6/07/15. https://doi.org/10.1016/j.ifacol.2015.10.246

TY - GEN

T1 - Using System Theory and Energy Methods to Prove Existence of Non-linear PDE's

AU - Zwart, Heiko J.

N1 - Conference code: 5

PY - 2015

Y1 - 2015

N2 - Consider a network with linear dynamics on the edges, and observation and control in the nodes. Assume that on the edges there is no damping, and so the dynamics can be described by an infinite-dimensional, port-Hamiltonian system. For general infinite-dimensional systems, the zero dynamics can be difficult to characterize and are sometimes ill-posed. However, for this class of systems the zero dynamics are shown to be well-defined. Using the underlying structure, simple characterizations and a constructive procedure can be obtained.

AB - Consider a network with linear dynamics on the edges, and observation and control in the nodes. Assume that on the edges there is no damping, and so the dynamics can be described by an infinite-dimensional, port-Hamiltonian system. For general infinite-dimensional systems, the zero dynamics can be difficult to characterize and are sometimes ill-posed. However, for this class of systems the zero dynamics are shown to be well-defined. Using the underlying structure, simple characterizations and a constructive procedure can be obtained.

KW - coupled wave equations

KW - EWI-26572

KW - zero dynamics

KW - Port-Hamiltonian system

KW - METIS-315602

KW - Distributed-parameter systems

KW - IR-99328

KW - Boundary control

KW - Networks

U2 - 10.1016/j.ifacol.2015.10.246

DO - 10.1016/j.ifacol.2015.10.246

M3 - Conference contribution

SN - 2405-8963

SP - 241

EP - 243

BT - 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015

PB - IFAC Proceedings

T2 - 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015

Y2 - 6 July 2015 through 7 July 2015

ER -