Authors

Yang Xia, Ji Xingmin

Abstract

A special kind of port-controlled bilinear Hamilton system is researched. The controllability distribution and observability codistribution of the kind of port-controlled bilinear Hamilton systems are disused by using differential geometric of nonlinear control system. Lie brackets between input vector field and control vector field, Lie derivative of output function along input vector field and control vector field are researed. At the same time, the controllability and observability of the port-controlled bilinear Hamilton systems are disused Lie brackets between input vector field and control vector field. Then the relation between the controllability and observability is studied. The equivalence condition of controllability and observability is given.

Citation

  • Journal: 2010 International Conference on Intelligent Computation Technology and Automation
  • Year: 2010
  • Volume:
  • Issue:
  • Pages: 1039–1042
  • Publisher: IEEE
  • DOI: 10.1109/icicta.2010.243

BibTeX

@inproceedings{Xia_2010,
  title={{Controllability and Observability of Bilinear Port-Controlled Hamiltonian Systems}},
  DOI={10.1109/icicta.2010.243},
  booktitle={{2010 International Conference on Intelligent Computation Technology and Automation}},
  publisher={IEEE},
  author={Xia, Yang and Xingmin, Ji},
  year={2010},
  pages={1039--1042}
}

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References

  • Nijmeijer, H. & van der Schaft, A. Nonlinear Dynamical Control Systems. (Springer New York, 1990). doi:10.1007/978-1-4757-2101-0 – 10.1007/978-1-4757-2101-0
  • isidori, Nonlinear Control Systems (0)
  • cheng, Geometric theory of nonlinear systems. (1987)
  • feng, Nonlinear Control Systems Analysis and Design (1998)
  • Maschke, B. M., van der Schaft, A. J. & Breedveld, P. C. An intrinsic Hamiltonian formulation of the dynamics of LC-circuits. IEEE Trans. Circuits Syst. I 42, 73–82 (1995) – 10.1109/81.372847
  • 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 schaft, Implicit Port-Controlled Hamiltonian Systems. J of the society of Instrument and Control Engineers of Janpan(SICE) (2000)
  • van der schaft, Port-controlled Hamiltonian Systems:Towards a Theory for Control and Design of Nonlinear Physical Systems. J of the society of Instrument and Control Engineers of Janpan(SICE) (2000)
  • Dalsmo, M. & van der Schaft, A. On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems. SIAM J. Control Optim. 37, 54–91 (1998) – 10.1137/s0363012996312039
  • van der Schaft, A. J., Dalsmo, M. & Maschke, B. M. Mathematical structures in the network representation of energy-conserving physical systems. Proceedings of 35th IEEE Conference on Decision and Control vol. 1 201–206 – 10.1109/cdc.1996.574296
  • blankenstein, Implicit Hamiltonian Systems Symmetry and Interconnection (2000)
  • maschke, Port-Controlled Hamiltonian Systems:Modelling Origins and System Theoretic Properties. IFAC Symp Nonlinear Control Systems Design (1992)
  • Blankenstein, G. & van der Schaft, A. J. Symmetry and reduction in implicit generalized Hamiltonian systems. Reports on Mathematical Physics 47, 57–100 (2001) – 10.1016/s0034-4877(01)90006-0