Asymptotic stabilization via control by interconnection of port-Hamiltonian systems

Authors

Fernando Castaños, Romeo Ortega, Arjan van der Schaft, Alessandro Astolfi

Abstract

We study the asymptotic properties of control by interconnection, a passivity-based controller design methodology for stabilization of port-Hamiltonian systems. It is well-known that the method, in its basic form, imposes some unnatural controller initialization to yield asymptotic stability of the desired equilibrium. We propose two different ways to overcome this restriction, one based on adaptation ideas, and the other one adding an extra damping injection to the controller. The analysis and design principles are illustrated through an academic example.

Keywords

Nonlinear control systems; Port-Hamiltonian systems; Asymptotic stability; Passivity-based control

Citation

• Journal: Automatica
• Year: 2009
• Volume: 45
• Issue: 7
• Pages: 1611–1618
• Publisher: Elsevier BV
• DOI: 10.1016/j.automatica.2009.03.015

BibTeX

@article{Casta_os_2009,
  title={{Asymptotic stabilization via control by interconnection of port-Hamiltonian systems}},
  volume={45},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2009.03.015},
  number={7},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Castaños, Fernando and Ortega, Romeo and van der Schaft, Arjan and Astolfi, Alessandro},
  year={2009},
  pages={1611--1618}
}

Download the bib file

References

• Barbashin, On stability of motion in the whole. Doklady Akademiya Nauk SSSR (N.S.) (1952)
• Cheng, D., Astolfi, A. & Ortega, R. On feedback equivalence to port controlled Hamiltonian systems. Systems & Control Letters vol. 54 911–917 (2005) – 10.1016/j.sysconle.2005.02.005
• Fujimoto, Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Systems and Control Letters (2003)
• error code: 50 – 10.1016/0016-0032(80)90026-5
• La Salle, (1961)
• Ortega, R., Jeltsema, D. & Scherpen, J. M. A. Power shaping: A new paradigm for stabilization of nonlinear RLC circuits. IEEE Transactions on Automatic Control vol. 48 1762–1767 (2003) – 10.1109/tac.2003.817918
• Ortega, R. & Spong, M. W. Adaptive motion control of rigid robots: A tutorial. Automatica vol. 25 877–888 (1989) – 10.1016/0005-1098(89)90054-x
• Ortega, R., van der Schaft, A., Castanos, F. & Astolfi, A. Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 53 2527–2542 (2008) – 10.1109/tac.2008.2006930
• Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• van der Schaft, (2000)
• Wang, Y., Feng, G. & Cheng, D. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica vol. 43 403–415 (2007) – 10.1016/j.automatica.2006.09.008