Skip to main content
Springer Nature Link
Log in

A family of adaptive H ∞ controllers with full information for dissipative hamiltonian systems

  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

This paper investigates a parameterization method of adaptive H ∞ controllers for dissipative Hamiltonian systems with disturbances and unknown parameters. The family of adaptive H ∞ controllers with full information is obtained by interconnecting an adaptive H ∞ controller with a generalized zero-energy-gradient (ZEG) detectable, free generalized Hamiltonian system. The present parameterization method avoids solving Hamilton-Jacobi-Issacs equations and thus the controllers obtained are easier in operation as compared to some existing ones. Simulations show the effectiveness and feasibility of the adaptive control strategy proposed in this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. B. M. Maschke, A. J. van der Schaft. Port-controlled hamiltonian systems: Modelling origins and system theoretic properties. In Proceedings of IFAC Symposium on nonlinear Control Systems, Bordeaux, France, pp. 282–288, 1992.

  2. A. J. van der Schaft, B. M. Maschke. The Hamiltonian formulation of energy conserving physical systems with external ports. Archive für Elektronik und Übertragungstechnik, vol. 49, no. 5–6, pp. 362–371, 1995.

    Google Scholar 

  3. A. Macchelli, C. Melchiorri. Modeling and control of the Timoshenko beam: The distributed port Hamiltonian approach. SIAM Journal on Control and Optimization, vol. 43, no. 2, pp. 743–767, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  4. Z. Xi, G. Feng, D. Cheng, Q. Lu. Nonlinear decentralized saturated controller design for power systems. IEEE Transactions on Control Systems Technology, vol. 11, no. 4, pp. 539–547, 2003.

    Article  Google Scholar 

  5. S. J. Li, Y. Z. Wang. Adaptive H-infinity control of synchronous generators with steam valve via Hamiltonian function method. Journal of Control Theory and Applications, vol. 4, no. 2, pp. 105–110, 2006.

    Article  MathSciNet  Google Scholar 

  6. Y. Z. Wang, D. Z. Cheng, Y. H. Liu, C. W. Li. Adaptive H ∞ excitation control of multi-machine power systems via Hamiltonian function method. International Journal of Control, vol. 77, no. 4, pp. 336–350, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  7. G. Escobar, A. J. van der Schaft, R. Ortega. A Hamiltonian viewpoint in the modeling of switching power converters. Automatica, vol. 35, no. 3, pp. 445–452, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  8. Y. Z. Wang, G. Feng, D. Z. Cheng, Y. H. Liu. Adaptive L 2 disturbance attenuation control of multi-machine power systems with SMES units. Automatica, vol. 42, no. 7, pp. 1121–1132, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  9. Y. Z. Wang, D. Z. Cheng, C. W. Li, Y. Ge. Dissipative Hamiltonian realization and energy-based L 2-disturbance attenuation control of multi-machine power systems. IEEE Transactions on Automatic Control, vol. 48, no. 8, pp. 1428–1433, 2003.

    Article  MathSciNet  Google Scholar 

  10. Y. Z. Wang, D. Z. Cheng, S. S. Ge. Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions. Systems & Control Letters, vol. 56, no. 2, pp. 141–149, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. C. Deng, H. N. Yu, A. Inoue. Decentralized PD control for non-uniform motion of a Hamiltonian hybrid system. International Journal of Automation and Computing, vol.5, no. 2, pp. 119–124, 2008.

    Article  Google Scholar 

  12. A. Isidori, A. Astolfi. Disturbance attenuation and H ∞ control via measurement feedback in nonlinear systems. IEEE Transactions on Automatic Control, vol. 37, no. 9, pp. 1283–1293, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  13. W.M. Lu, J. C. Doyle. H ∞ control of nonlinear systems via output feedback: Controller parameterization. In Proceedings of the 32nd IEEE Conference on Decision and Control, IEEE, San Antonio, USA, vol. 1, pp. 166–171, 1993.

    Google Scholar 

  14. C. F. Yung, Y. P. Lin, F. B. Yeh. A family of nonlinear H ∞ output feedback controllers. IEEE Transactions on Automatic Control, vol. 41, no. 2, pp. 232–236, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  15. C. F. Yung, J. L. Wu, T. T. Lee. Parameterization of nonlinear H ∞ state-feedback controllers. Automatica, vol. 33, no. 8, pp. 1587–1590, 1997.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, PRC

    Song Xu & Xiao-Rong Hou

  2. Faculty of Science, Ningbo University, Ningbo, 315211, PRC

    Song Xu

Authors
  1. Song Xu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Xiao-Rong Hou
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Xiao-Rong Hou.

Additional information

This work was supported by National Natural Science Foundation of China (No. 61074189).

Song Xu received the M. Sc. degree from the College of Natural Science, Nanjing University of Aeronautics and Astronautics, Nanjing, PRC in 2004. He is currently a lecturer at the Faculty of Science, Ningbo University and a Ph.D. candidate at the School of Automation Engineering, University of Electronic Science and Technology of China.

His research interests include nonlinear control systems and controlled Hamiltonian systems.

Xiao-Rong Hou is a professor of mathematics and computer science at University of Electronic Science and Technology of China.

His research interests include symbolic computation, real algebraic geometry, control theory, and intelligent systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, S., Hou, XR. A family of adaptive H ∞ controllers with full information for dissipative hamiltonian systems. Int. J. Autom. Comput. 8, 209–214 (2011). https://doi.org/10.1007/s11633-011-0575-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-011-0575-3

Keywords