Infinite-dimensional port-Hamiltonian systems: a system node approach

We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes as reported by Staffans (Well-posed linear systems. Encyclopedia of mathematics and its applications, Cambridge University Press, Cambridge, UK, 2005)...

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Published in:	Mathematics of control, signals, and systems Vol. 37; no. 3; pp. 573 - 620
Main Authors:	Philipp, Friedrich M., Reis, Timo, Schaller, Manuel
Format:	Journal Article
Language:	English
Published:	London Springer London 01.09.2025 Springer Nature B.V
Subjects:	Communications Engineering Control Energy Hamiltonian functions Hilbert space Hyperbolic systems Linear systems Mathematics Mathematics and Statistics Mechatronics Networks Ordinary differential equations Original Article Partial differential equations Robotics System theory Systems Theory Boundary control Infinite-dimensional systems System nodes Port-Hamiltonian systems
ISSN:	0932-4194, 1435-568X
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Abstract	We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes as reported by Staffans (Well-posed linear systems. Encyclopedia of mathematics and its applications, Cambridge University Press, Cambridge, UK, 2005) to formulate a suitable concept for port-Hamiltonian systems, which allows a unifying approach to systems with boundary as well as distributed control and observation. The concept presented in this article is further neither limited to parabolic nor hyperbolic systems, and it also covers partial differential equations on multi-dimensional spatial domains. Our presented theory is substantiated by means of several physical examples.
AbstractList	We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes as reported by Staffans (Well-posed linear systems. Encyclopedia of mathematics and its applications, Cambridge University Press, Cambridge, UK, 2005) to formulate a suitable concept for port-Hamiltonian systems, which allows a unifying approach to systems with boundary as well as distributed control and observation. The concept presented in this article is further neither limited to parabolic nor hyperbolic systems, and it also covers partial differential equations on multi-dimensional spatial domains. Our presented theory is substantiated by means of several physical examples. We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes as reported by Staffans (Well-posed linear systems. Encyclopedia of mathematics and its applications, Cambridge University Press, Cambridge, UK, 2005) to formulate a suitable concept for port-Hamiltonian systems, which allows a unifying approach to systems with boundary as well as distributed control and observation. The concept presented in this article is further neither limited to parabolic nor hyperbolic systems, and it also covers partial differential equations on multi-dimensional spatial domains. Our presented theory is substantiated by means of several physical examples.
Author	Philipp, Friedrich M. Reis, Timo Schaller, Manuel
Author_xml	– sequence: 1 givenname: Friedrich M. surname: Philipp fullname: Philipp, Friedrich M. organization: Optimization-Based Control Group, Technische Universität Ilmenau – sequence: 2 givenname: Timo surname: Reis fullname: Reis, Timo organization: Systems Theory and Partial Differential Equations Group, Technische Universität Ilmenau – sequence: 3 givenname: Manuel surname: Schaller fullname: Schaller, Manuel email: manuel.schaller@math.tu-chemnitz.de organization: Faculty of Mathematics, Chemnitz University of Technology
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Cites_doi	10.1090/surv/015 10.1016/S0022-247X(02)00455-9 10.1137/20M1371166 10.1137/15M1024901 10.1007/978-3-030-36714-5 10.1137/110831726 10.1007/978-3-030-35898-3_4 10.1007/978-3-7643-8994-9 10.1007/978-3-0348-0399-1 10.1137/1.9781611972597 10.1090/S0033-569X-06-00994-7 10.1109/LCSYS.2019.2916814 10.1007/978-3-319-32062-5 10.1016/j.automatica.2013.11.035 10.1109/CDC40024.2019.9030180 10.1017/CBO9780511543197 10.1016/j.automatica.2019.02.010 10.1007/s00498-018-0223-3 10.1137/20M1366216 10.1137/040611677 10.1137/120869444 10.1007/s00498-023-00349-2 10.1016/j.sysconle.2023.105564 10.1561/2600000002 10.1137/18M1181304 10.3934/eect.2020098 10.1016/S0393-0440(01)00083-3 10.3934/eect.2014.3.207 10.1016/j.ifacol.2021.11.078 10.1007/s00020-024-02780-9 10.1007/s004980200012 10.1016/j.ifacol.2021.11.082
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Title	Infinite-dimensional port-Hamiltonian systems: a system node approach
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