Port-Hamiltonian Systems with Several Space Variables: Dressing, Explicit Solutions and Energy Relations
Authors
Abstract
No available
Citation
- Journal: SSRN Electronic Journal
- Year: 2022
- Volume:
- Issue:
- Pages:
- Publisher: Elsevier BV
- DOI: 10.2139/ssrn.4185438
BibTeX
@article{Sakhnovich_2022,
title={{Port-Hamiltonian Systems with Several Space Variables: Dressing, Explicit Solutions and Energy Relations}},
ISSN={1556-5068},
DOI={10.2139/ssrn.4185438},
journal={SSRN Electronic Journal},
publisher={Elsevier BV},
author={Sakhnovich, Alexander},
year={2022}
}
References
- Benner, P., Goyal, P. & Van Dooren, P. Identification of port-Hamiltonian systems from frequency response data. Systems & Control Letters 143, 104741 (2020) – 10.1016/j.sysconle.2020.104741
- J L Cieslinski, Algebraic construction of the Darboux matrix revisited. J. Phys. A (2009)
- Constantin, A. & Ivanov, R. Dressing Method for the Degasperis–Procesi Equation. Stud Appl Math 138, 205–226 (2016) – 10.1111/sapm.12149
- Gernandt, H., Haller, F. E., Reis, T. & Schaft, A. J. van der. Port-Hamiltonian formulation of nonlinear electrical circuits. Journal of Geometry and Physics 159, 103959 (2021) – 10.1016/j.geomphys.2020.103959
- Gesztesy, F. A Complete Spectral Characterization of the Double Commutation Method. Journal of Functional Analysis 117, 401–446 (1993) – 10.1006/jfan.1993.1132
- Gesztesy, F. & Teschl, G. On the double commutation method. Proc. Amer. Math. Soc. 124, 1831–1840 (1996) – 10.1090/s0002-9939-96-03299-6
- C H Gu, Darboux transformations in integrable systems. Theory and their applications to geometry (2005)
- Jacob, B., Morris, K. & Zwart, H. C 0-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain. J. Evol. Equ. 15, 493–502 (2015) – 10.1007/s00028-014-0271-1
- Jacob, B. & Zwart, H. J. Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces. (Springer Basel, 2012). doi:10.1007/978-3-0348-0399-1 – 10.1007/978-3-0348-0399-1
- Kaashoek, M. A. & Sakhnovich, A. L. Discrete skew self-adjoint canonical system and the isotropic Heisenberg magnet model. Journal of Functional Analysis 228, 207–233 (2005) – 10.1016/j.jfa.2004.10.022
- Kostenko, A., Sakhnovich, A. & Teschl, G. Commutation methods for Schrödinger operators with strongly singular potentials. Mathematische Nachrichten 285, 392–410 (2011) – 10.1002/mana.201000108
- Le Gorrec, Y. & Matignon, D. Coupling between hyperbolic and diffusive systems: A port-Hamiltonian formulation. European Journal of Control 19, 505–512 (2013) – 10.1016/j.ejcon.2013.09.003
- Marchenko, V. A. Nonlinear Equations and Operator Algebras. Mathematics and Its Applications (Springer Netherlands, 1988). doi:10.1007/978-94-009-2887-9 – 10.1007/978-94-009-2887-9
- Mattioni, A., Wu, Y., Le Gorrec, Y. & Zwart, H. Stabilization of a class of mixed ODE–PDE port-Hamiltonian systems with strong dissipation feedback. Automatica 142, 110284 (2022) – 10.1016/j.automatica.2022.110284
- Medianu, S. & Lefèvre, L. Structural identifiability of linear Port Hamiltonian systems. Systems & Control Letters 151, 104915 (2021) – 10.1016/j.sysconle.2021.104915
- Moreschini, A., Mattioni, M., Monaco, S. & Normand-Cyrot, D. Stabilization of Discrete Port-Hamiltonian Dynamics via Interconnection and Damping Assignment. IEEE Control Syst. Lett. 5, 103–108 (2021) – 10.1109/lcsys.2020.3000705
- Matveev, V. B. & Salle, M. A. Darboux Transformations and Solitons. Springer Series in Nonlinear Dynamics (Springer Berlin Heidelberg, 1991). doi:10.1007/978-3-662-00922-2 – 10.1007/978-3-662-00922-2
- Mennicken, R., Sakhnovich, A. L. & Tretter, C. Direct and inverse spectral problem for a system of differential equations depending rationally on the spectral parameter. Duke Math. J. 109, (2001) – 10.1215/s0012-7094-01-10931-9
- R Miura, B�cklund Transformations (1976)
- R Ortega, Stabilization of portcontrolled Hamiltonian systems via energy balancing. Lect. Notes Control Inf. Sci (1999)
- Sakhnovich, A. L. Dressing procedure for solutions of non-linear equations and the method of operator identities. Inverse Problems 10, 699–710 (1994) – 10.1088/0266-5611/10/3/013
- Sakhnovich, A. Construction of the Solution of the Inverse Spectral Problem for a System Depending Rationally on the Spectral Parameter, Borg–Marchenko-Type Theorem and Sine-Gordon Equation. Integr. Equ. Oper. Theory 69, 567–600 (2010) – 10.1007/s00020-010-1843-2
- Sakhnovich, A. Dynamical canonical systems and their explicit solutions. Discrete & Continuous Dynamical Systems - A 37, 1679–1689 (2017) – 10.3934/dcds.2017069
- A L Sakhnovich, Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications (2022)
- A L Sakhnovich, Inverse Problems and Nonlinear Evolution Equations. Solutions, Darboux Matrices and Weyl-Titchmarsh Functions (2013)
- L A Sakhnovich, On the factorization of the transfer matrix function. Sov. Math. Dokl (1976)
- Sakhnovich, L. A. Spectral Theory of Canonical Differential Systems. Method of Operator Identities. (Birkhäuser Basel, 1999). doi:10.1007/978-3-0348-8713-7 – 10.1007/978-3-0348-8713-7
- van der Schaft, A. & Maschke, B. Generalized port-Hamiltonian DAE systems. Systems & Control Letters 121, 31–37 (2018) – 10.1016/j.sysconle.2018.09.008
- J A Villegas, A Port-Hamiltonian Approach to Distributed Parameter Systems, thesis (2007)
- Wu, Y., Hamroun, B., Le Gorrec, Y. & Maschke, B. Reduced Order LQG Control Design for Infinite Dimensional Port Hamiltonian Systems. IEEE Trans. Automat. Contr. 66, 865–871 (2021) – 10.1109/tac.2020.2997373
- V E Zakharov, On the integrability of classical spinor models in two-dimensional space-time. Oskar-Morgenstern-Platz (1980)