L<inf>2</inf>-gain of Port-Hamiltonian systems and application to a biochemical fermenter model

Authors

Jorgen K. Johnsen, Florian Dorfler, Frank Allgower

Abstract

We consider the Lscr2-gain of nonlinear Port-Hamiltonian systems. Using the Hamiltonian and an additional scaling matrix, we show that an upper bound on the Lscr2-gain can be computed by solving a matrix inequality. The Lscr2-gain is typically used in combination with the small-gain theorem. In particular it can be used to guarantee robust stability with respect to gain-bounded model uncertainties. This application of the Lscr2-gain is demonstrated with a biochemical fermentation process where the specific cell growth rate is unknown but contained in a parameter interval.

Citation

Journal: 2008 American Control Conference
Year: 2008
Volume:
Issue:
Pages: 153–158
Publisher: IEEE
DOI: 10.1109/acc.2008.4586483

BibTeX

@inproceedings{Johnsen_2008,
  title={{L&lt;inf&gt;2&lt;/inf&gt;-gain of Port-Hamiltonian systems and application to a biochemical fermenter model}},
  DOI={10.1109/acc.2008.4586483},
  booktitle={{2008 American Control Conference}},
  publisher={IEEE},
  author={Johnsen, Jorgen K. and Dorfler, Florian and Allgower, Frank},
  year={2008},
  pages={153--158}
}

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References

hangos, Analysis and Control of Nonlinear Process Systems (2004)
(0)
Gahinet, P. & Apkarian, P. A linear matrix inequality approach toH∞control. International Journal of Robust and Nonlinear Control vol. 4 421–448 (1994) – 10.1002/rnc.4590040403
Kaszkurewicz, E. & Bhaya, A. Matrix Diagonal Stability in Systems and Computation. (Birkhäuser Boston, 2000). doi:10.1007/978-1-4612-1346-8 – 10.1007/978-1-4612-1346-8
Arcak, M. & Sontag, E. D. Diagonal stability of a class of cyclic systems and its connection with the secant criterion. Automatica vol. 42 1531–1537 (2006) – 10.1016/j.automatica.2006.04.009
Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
Cervera, J., van der Schaft, A. J. & Baños, A. Interconnection of port-Hamiltonian systems and composition of Dirac structures. Automatica vol. 43 212–225 (2007) – 10.1016/j.automatica.2006.08.014
maschke, modeling and control of physical systems: an approach based on energy and interconnection. Proc 14th MTNS Perpignan (2000)
Fossas, E., Ros, R. M. & Sira-Ramírez, H. Passivity-Based Control of a Bioreactor System. Journal of Mathematical Chemistry vol. 36 347–360 (2004) – 10.1023/b:jomc.0000044522.36742.4b
Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Euler-Lagrange systems. Communications and Control Engineering 15–37 (1998) doi:10.1007/978-1-4471-3603-3_2 – 10.1007/978-1-4471-3603-3_2
Johnsen, J. K. & Allöwer, F. Interconnection and Damping Assignment Passivity-Based Control of a Four-Tank System. Lecture Notes in Control and Information Sciences 111–122 doi:10.1007/978-3-540-73890-9_8 – 10.1007/978-3-540-73890-9_8
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
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, 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
khalil, Nonlinear Systems (2002)