Port-Hamiltonian Formulation of Systems With Memory
Authors
Dimitri Jeltsema, Arnau Doria-Cerezo
Abstract
In this paper, we consider memristors, meminductors, and memcapacitors and their properties as port-Hamiltonian systems. The port-Hamiltonian formalism naturally arises from network modeling of physical systems in a variety of domains. Exposing the relation between the energy storage, dissipation, and interconnection structure, this framework underscores the physics of the system. One of the strong aspects of the port-Hamiltonian formalism is that a power-preserving interconnection between port-Hamiltonian systems results in another port-Hamiltonian system with composite energy, dissipation, and interconnection structure. This feature can advantageously be used to model, analyze, and simulate networks consisting of complex interconnections of both conventional and memory circuit elements. Furthermore, the port-Hamiltonian formalism naturally extends the fundamental properties of the memory elements beyond the realm of electrical circuits.
Citation
- Journal: Proceedings of the IEEE
- Year: 2012
- Volume: 100
- Issue: 6
- Pages: 1928–1937
- Publisher: Institute of Electrical and Electronics Engineers (IEEE)
- DOI: 10.1109/jproc.2011.2164169
BibTeX
@article{Jeltsema_2012,
title={{Port-Hamiltonian Formulation of Systems With Memory}},
volume={100},
ISSN={1558-2256},
DOI={10.1109/jproc.2011.2164169},
number={6},
journal={Proceedings of the IEEE},
publisher={Institute of Electrical and Electronics Engineers (IEEE)},
author={Jeltsema, Dimitri and Doria-Cerezo, Arnau},
year={2012},
pages={1928--1937}
}
References
- Jeltsema, D. & van der Schaft, A. J. Memristive port-Hamiltonian Systems. Mathematical and Computer Modelling of Dynamical Systems vol. 16 75–93 (2010) – 10.1080/13873951003690824
- Oster, G. F. & Auslander, D. M. The Memristor: A New Bond Graph Element. Journal of Dynamic Systems, Measurement, and Control vol. 94 249–252 (1972) – 10.1115/1.3426595
- Pershin, Y. V., La Fontaine, S. & Di Ventra, M. Memristive model of amoeba learning. Physical Review E vol. 80 (2009) – 10.1103/physreve.80.021926
- Smith, M. C. Synthesis of mechanical networks: the inerter. IEEE Transactions on Automatic Control vol. 47 1648–1662 (2002) – 10.1109/tac.2002.803532
- Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. The missing memristor found. Nature vol. 453 80–83 (2008) – 10.1038/nature06932
- Stulov, A. Hysteretic model of the grand piano hammer felt. The Journal of the Acoustical Society of America vol. 97 2577–2585 (1995) – 10.1121/1.411912
- sse, Theoretische Grundlagen Der Elektrotechnik (2005)
- van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
- Chua, L. O. & Szeto, E. W. High‐order non‐linear circuit elements: Circuit‐theoretic properties. International Journal of Circuit Theory and Applications vol. 11 187–206 (1983) – 10.1002/cta.4490110206
- Chua, L. O. & Sung Mo Kang. Memristive devices and systems. Proceedings of the IEEE vol. 64 209–223 (1976) – 10.1109/proc.1976.10092
- Di Ventra, M., Pershin, Y. V. & Chua, L. O. Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors. Proceedings of the IEEE vol. 97 1717–1724 (2009) – 10.1109/jproc.2009.2021077
- Civelek, C. Mathematical modelling of rotational mechanical elements of higher order and their characteristics. Mathematical and Computer Modelling vol. 43 957–964 (2006) – 10.1016/j.mcm.2005.09.023
- Jeltsema, D. & Doria-Cerezo, A. Mechanical memory elements: Modeling of systems with position-dependent mass revisited. 49th IEEE Conference on Decision and Control (CDC) 3511–3516 (2010) doi:10.1109/cdc.2010.5717274 – 10.1109/cdc.2010.5717274
- Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
- Chua, L. O. Nonlinear circuit foundations for nanodevices, part I: the four-element torus. Proceedings of the IEEE vol. 9 1830–1859 (2003) – 10.1109/jproc.2003.818319
- Chua, L. Memristor-The missing circuit element. IEEE Transactions on Circuit Theory vol. 18 507–519 (1971) – 10.1109/tct.1971.1083337
- Multidomain modeling of nonlinear networks and systems. IEEE Control Systems vol. 29 28–59 (2009) – 10.1109/mcs.2009.932927