Estimation of the output deviation norm for uncertain, discrete-time nonlinear systems in a state dependent form

Przemysław Orłowski

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 4, page 505-513
  • ISSN: 1641-876X

Abstract

top
Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems given in the state space dependent form. The method for numerical estimation of the maximal norm of the output trajectory deviation with applications to robust control synthesis is proposed based on the introduced three-term additive uncertainty model. Theoretical deliberations are complemented with a numerical, water-tank system example.

How to cite

top

Orłowski, Przemysław. "Estimation of the output deviation norm for uncertain, discrete-time nonlinear systems in a state dependent form." International Journal of Applied Mathematics and Computer Science 17.4 (2007): 505-513. <http://eudml.org/doc/207855>.

@article{Orłowski2007,
abstract = {Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems given in the state space dependent form. The method for numerical estimation of the maximal norm of the output trajectory deviation with applications to robust control synthesis is proposed based on the introduced three-term additive uncertainty model. Theoretical deliberations are complemented with a numerical, water-tank system example.},
author = {Orłowski, Przemysław},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {uncertain systems; uncertain estimates; discrete-time systems; nonlinear systems},
language = {eng},
number = {4},
pages = {505-513},
title = {Estimation of the output deviation norm for uncertain, discrete-time nonlinear systems in a state dependent form},
url = {http://eudml.org/doc/207855},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Orłowski, Przemysław
TI - Estimation of the output deviation norm for uncertain, discrete-time nonlinear systems in a state dependent form
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 4
SP - 505
EP - 513
AB - Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems given in the state space dependent form. The method for numerical estimation of the maximal norm of the output trajectory deviation with applications to robust control synthesis is proposed based on the introduced three-term additive uncertainty model. Theoretical deliberations are complemented with a numerical, water-tank system example.
LA - eng
KW - uncertain systems; uncertain estimates; discrete-time systems; nonlinear systems
UR - http://eudml.org/doc/207855
ER -

References

top
  1. Albertini F., Sontag E. D. (1994): Further results on controllability properties of discrete-time nonlinear systems. Dynamics and Control, Vol. 4, No. 3, pp. 235-253. Zbl0808.93004
  2. Basar T. and Bernhard P. (1995): H_[∞]-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach, 2nd Ed., Boston: Birkhauser. Zbl0835.93001
  3. Bacic M., Cannon M., Kouvarakis B. (2003): Constrained NMPC via state-space partitioning for input affinite non-linear systems. International Journal of Control. Vol. 76, No. 15, pp. 1516-1526. Zbl1048.93037
  4. Dai J., Mao J., (2002): Robust flight controller design for helicopters based on genetic algorithms, Proceedings of the 15th IFAC World Congress, Barcelona 2002, (on CD-ROM) 
  5. Dutka, A., Ordys A. (2004): The optimal nonlinear generalised predictive control by the time-varying approximation. Proceeding of the Conference Methods and Model in Automation and Robotics, Międzyzdroje, Poland, pp. 299-304. 
  6. Grancharova A., Johansen T., Tondel P. (2005): Computational aspects of approximate explict nonlinear model predictive control. In: Lecture Notes in Control and Information Sciences vol. 358/2007: Assessment and Future Directions of Nonlinear Model Predictive Control, Springer Berlin/Heidelberg, pp. 181-192. Zbl1223.93030
  7. Impram S. T., Munro N. (2001): Describing functions in nonlinear systems with structured and unstructured uncertainties. International Journal of Control. Vol. 74, No. 6, pp. 600-608. Zbl1086.93505
  8. Kouvarakis B., Cannon M., Rosser J. A. (1999): Nonlinear model based predictive control, International Journal of Control, Vol. 72, No. 10, pp. 919-928. 
  9. Lee Y. I., Kouvarakis B., Cannon M. (2002): Constrained receding horizon predictive control for nonlinear systems, Automatica, Vol. 38, No. 12, pp. 2093-2102. Zbl1017.93043
  10. Lewis F. L. (1986): Optimal Control. John Wiley and Sons, New York. 
  11. Ordys A. W., and Clarke D. W. (1993): A state-space description for GPC controllers. International Journal of Systems Science, Vol. 24, No. 9, pp. 1727-1744. Zbl0788.93008
  12. Orłowski P. (2001): Applications of discrete evolution operators in time-varying systems. Proceedings of the European Control Conference, Porto, Portugal, pp. 3259-3264. 
  13. Orłowski, P. (2003): Robust control design for a class of non-linear systems. Proceedings of the Process Control PC'03 Conference, Strbske Pleso, Slovakia, CD-ROM. 
  14. Orłowski P. (2004): Selected problems of frequency analysis for time-varying discrete-time systems using singular value decomposition and discrete Fourier transform. Journal of Sound and Vibration, Vol. 278, No. 4-5, pp. 903-921. 
  15. Orłowski P. (2006): Methods for stability evaluation for linear time varying, discrete-time systems on finite time horizon. International Journal of Control, Vol. 79, No. 3, pp. 249-262. Zbl1122.93379
  16. Postlethwae I., Tsai M. C and Gu D. W. (1990): Weighting function selection in Hinf design. Proceedings of the IFAC Word Congress, Tallinn, Estonia, pp. 104-109. 
  17. Tang, K. S., Man K. F., and Gu D. W. (1996): Structured genetic algorithm for robust H1 control systems design, IEEE Transactions on Industrial Electronics, Vol. 43, No. 5, pp. 575-582. 
  18. Whidborne, J. F., Postlethwaite I. and Gu D. W. (1994): Robust controller design using Hinf loop-shaping and the method of inequalities, IEEE Transactions on Control Systems Technology, Vol. 29, No. 4, pp. 455-461. 
  19. Van der Schaft, A. J. (1992): L_2-gain analysis of nonlinear systems and nonlinear state feedback H control, IEEE Transactions on Automatic Control, Vol. AC-37, No. 6, pp. 770-784. Zbl0755.93037
  20. Yang C. D., Tai H. C., and Lee C. C. (1997): Experimental approach to selecting Hinf weighting functions for DC servos. Journal of Dynamic Systems, Measurement and Control, Vol. 119, No. 1, pp. 101-105. Zbl1053.93506
  21. Zhou, K., Doyle, J. C., and Glover, K. (1996): Robust and Optimal Control, Englewood Cliffs, NJ: Prentice Hall Zbl0999.49500

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.