Dynamic extension is unnecessary for stabilization via interconnection and damping assignment passivity-based control

Authors

Abstract

Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a technique that regulates the behavior of nonlinear systems assigning a desired (Port Hamiltonian) structure to the closed-loop. This basic idea, introduced seven years ago, has turned out to be very successful and has provided solutions to a wide variety of physical problems. Although IDA-PBC is originally formulated as a static state-feedback technique a natural question that arises is whether it is possible to extend the realm of applicability of the method by considering dynamic controllers. More precisely, is the set of plants that is stabilizable with static state-feedback IDA-PBC smaller than the one stabilizable with dynamic IDA-PBC? The main contribution of this paper is to prove that the answer to this question is, unfortunately, negative.

Keywords

Passivity-based control; Stabilization; Nonlinear systems

Citation

Journal: Systems & Control Letters
Year: 2009
Volume: 58
Issue: 2
Pages: 133–135
Publisher: Elsevier BV
DOI: 10.1016/j.sysconle.2008.09.006

BibTeX

@article{Astolfi_2009,
  title={{Dynamic extension is unnecessary for stabilization via interconnection and damping assignment passivity-based control}},
  volume={58},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2008.09.006},
  number={2},
  journal={Systems &amp; Control Letters},
  publisher={Elsevier BV},
  author={Astolfi, Alessandro and Ortega, Romeo},
  year={2009},
  pages={133--135}
}

Download the bib file

References

Auckly, D., Kapitanski, L. & White, W. Control of nonlinear underactuated systems. Communications on Pure and Applied Mathematics vol. 53 354–369 (2000) – 10.1002/(sici)1097-0312(200003)53:3<354::aid-cpa3>3.0.co;2-u
Bloch, A. M., Leonard, N. E. & Marsden, J. E. Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem. IEEE Transactions on Automatic Control vol. 45 2253–2270 (2000) – 10.1109/9.895562
Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters vol. 42 217–227 (2001) – 10.1016/s0167-6911(00)00091-8
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
Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Transactions on Automatic Control vol. 47 1218–1233 (2002) – 10.1109/tac.2002.800770
Ortega, R. & García-Canseco, E. Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control vol. 10 432–450 (2004) – 10.3166/ejc.10.432-450
van der Schaft, Nonlinear state space H∞ control theory. (1993)
van der Schaft, (1999)