Balanced Realization and Model Order Reduction for Port-Hamiltonian Systems

Authors

Kenji FUJIMOTO

Abstract

This paper is concerned with nonlinear model order reduction for electro-mechanical systems described by port-Hamiltonian formulae. A novel weighted balacend realization and model order reduction procedure is proposed which preserves port-Hamiltonian structure as well as stability, reachability and observability of the original system. This implies that one can utilize the intrinsic physical properties such as physical energy and the corresponding dissipativity for the reduced order model. Further, the proposed method reduces the computational effort in solving partial differential equations for nonlinear balanced realization. A numerical simulation shows how the proposed method works.

Citation

• Journal: Journal of System Design and Dynamics
• Year: 2008
• Volume: 2
• Issue: 3
• Pages: 694–702
• Publisher: Japan Society of Mechanical Engineers
• DOI: 10.1299/jsdd.2.694

BibTeX

@article{FUJIMOTO_2008,
  title={{Balanced Realization and Model Order Reduction for Port-Hamiltonian Systems}},
  volume={2},
  ISSN={1881-3046},
  DOI={10.1299/jsdd.2.694},
  number={3},
  journal={Journal of System Design and Dynamics},
  publisher={Japan Society of Mechanical Engineers},
  author={FUJIMOTO, Kenji},
  year={2008},
  pages={694--702}
}

Download the bib file

References

• Fujimoto, K. What are singular values of nonlinear operators? 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) 1623-1628 Vol.2 (2004) doi:10.1109/cdc.2004.1430277 – 10.1109/cdc.2004.1430277
• Fujimoto, K. & Scherpen, J. M. A. Singular value analysis of Hankel operators for general nonlinear systems. 2003 European Control Conference (ECC) 719–724 (2003) doi:10.23919/ecc.2003.7085041 – 10.23919/ecc.2003.7085041
• Fujimoto, K. & Scherpen, J. M. A. Nonlinear input-normal realizations based on the differential eigenstructure of Hankel operators. IEEE Trans. Automat. Contr. 50, 2–18 (2005) – 10.1109/tac.2004.840476
• Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters 42, 217–227 (2001) – 10.1016/s0167-6911(00)00091-8
• FUJIMOTO KENJI, (2006)
• Fujimoto, K. & Tsubakino, D. Computation of nonlinear balanced realization and model reduction based on Taylor series expansion. Systems & Control Letters 57, 283–289 (2008) – 10.1016/j.sysconle.2007.08.015
• HAHN J, (2000)
• Lopezlena, R., Scherpen, J. M. A. & Fujimoto, K. Energy-Storage Balanced Reduction of Port-Hamiltonian Systems. IFAC Proceedings Volumes 36, 69–74 (2003) – 10.1016/s1474-6670(17)38869-9
• Newman, A. J. & Krishnaprasad, P. S. Computation for nonlinear balancing. Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171) vol. 4 4103–4104 – 10.1109/cdc.1998.761942
• Obinata, G. & Anderson, B. D. O. Model Reduction for Control System Design. Communications and Control Engineering (Springer London, 2001). doi:10.1007/978-1-4471-0283-0 – 10.1007/978-1-4471-0283-0
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38, 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Scherpen, J. M. A. Balancing for nonlinear systems. Systems & Control Letters 21, 143–153 (1993) – 10.1016/0167-6911(93)90117-o
• Gray, W. S. & Scherpen, J. M. A. Minimality and local state decompositions of a nonlinear state space realization using energy functions. IEEE Trans. Automat. Contr. 45, 2079–2086 (2000) – 10.1109/9.887630
• SCHERPEN, J. M. A. & VAN DER SCHAFT, A. J. Normalized coprime factorizations and balancing for unstable nonlinear systems. International Journal of Control 60, 1193–1222 (1994) – 10.1080/00207179408921517
• 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
• van der Vorst, H. A. Iterative Krylov Methods for Large Linear Systems. (2003) doi:10.1017/cbo9780511615115 – 10.1017/cbo9780511615115