Authors

Krishna C. Kosaraju, Yu Kawano, Jacquelien M.A. Scherpen

Abstract

In this paper we introduce a new notion of passivity which we call Krasovskii’s passivity and provide a sufficient condition for a system to be Krasovskii’s passive. Based on this condition, we investigate classes of port-Hamiltonian and gradient systems which are Krasovskii’s passive. Moreover, we provide a new interconnection based control technique based on Krasovskii’s passivity. Our proposed control technique can be used even in the case when it is not clear how to construct the standard passivity based controller, which is demonstrated by examples of a Boost converter and a parallel RLC circuit.

Keywords

Nonlinear systems; passivity; controller design

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2019
  • Volume: 52
  • Issue: 16
  • Pages: 466–471
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2019.12.005
  • Note: 11th IFAC Symposium on Nonlinear Control Systems NOLCOS 2019- Vienna, Austria, 4–6 September 2019

BibTeX

@article{Kosaraju_2019,
  title={{Krasovskii’s Passivity}},
  volume={52},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2019.12.005},
  number={16},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Kosaraju, Krishna C. and Kawano, Yu and Scherpen, Jacquelien M.A.},
  year={2019},
  pages={466--471}
}

Download the bib file

References

  • Angeli, D. Systems With Counterclockwise Input–Output Dynamics. IEEE Transactions on Automatic Control vol. 51 1130–1143 (2006) – 10.1109/tac.2006.878747
  • Boyd, (2004)
  • Cortés, J., van der Schaft, A. & Crouch, P. E. Characterization of Gradient Control Systems. SIAM Journal on Control and Optimization vol. 44 1192–1214 (2005) – 10.1137/s0363012903425568
  • Feijer, D. & Paganini, F. Stability of primal–dual gradient dynamics and applications to network optimization. Automatica vol. 46 1974–1981 (2010) – 10.1016/j.automatica.2010.08.011
  • Forni, F. & Sepulchre, R. A Differential Lyapunov Framework for Contraction Analysis. IEEE Transactions on Automatic Control vol. 59 614–628 (2014) – 10.1109/tac.2013.2285771
  • Forni, F., Sepulchre, R. & van der Schaft, A. J. On differential passivity of physical systems. 52nd IEEE Conference on Decision and Control 6580–6585 (2013) doi:10.1109/cdc.2013.6760930 – 10.1109/cdc.2013.6760930
  • Hill, D. J. & Moylan, P. J. Dissipative Dynamical Systems: Basic Input-Output and State Properties. Journal of the Franklin Institute vol. 309 327–357 (1980) – 10.1016/0016-0032(80)90026-5
  • Jeltsema, D. & Scherpen, J. M. A. Tuning of Passivity-Preserving Controllers for Switched-Mode Power Converters. IEEE Transactions on Automatic Control vol. 49 1333–1344 (2004) – 10.1109/tac.2004.832236
  • Khalil, (1996)
  • Kosaraju, K. C., Chinde, V., Pasumarthy, R., Kelkar, A. & Singh, N. M. Stability Analysis of Constrained Optimization Dynamics via Passivity Techniques. IEEE Control Systems Letters vol. 2 91–96 (2018) – 10.1109/lcsys.2017.2750480
  • Kosaraju, (2017)
  • Kosaraju, (2018)
  • Kosaraju, (2018)
  • Kundur, (1994)
  • Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
  • Ortega, (2013)
  • Simpson-Porco, (2018)
  • Sira-Ramirez, (2006)
  • Stegink, T., De Persis, C. & van der Schaft, A. A Unifying Energy-Based Approach to Stability of Power Grids With Market Dynamics. IEEE Transactions on Automatic Control vol. 62 2612–2622 (2017) – 10.1109/tac.2016.2613901
  • van der Schaft, A. J. Observability and Controllability for Smooth Nonlinear Systems. SIAM Journal on Control and Optimization vol. 20 338–354 (1982) – 10.1137/0320026
  • van der Schaft, (2000)
  • van der Schaft, On the relation between port-Hamiltonian and gradient systems. Preprints of the 18th IFAC World Congress (2011)
  • van der Schaft, On diferential passivity (2013)
  • Willems, J. C. Dissipative dynamical systems Part II: Linear systems with quadratic supply rates. Archive for Rational Mechanics and Analysis vol. 45 352–393 (1972) – 10.1007/bf00276494