State Dependant Anytime Control  Methodology for  Non-Linear Systems

Annamária R. Várkonyi-Kóczy

doi:10.20965/jaciii.2008.p0198

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JACIII Vol.12 No.2 pp. 198-205

doi: 10.20965/jaciii.2008.p0198

(2008)

Paper:

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State Dependant Anytime Control Methodology for Non-Linear Systems

Annamária R. Várkonyi-Kóczy

Dept. of Measurement and Information Systems, Budapest University of Technology and Economics, Magyar tudósok körútja 2. H-1521 Budapest, Hungary

Received:

September 7, 2007

Accepted:

November 7, 2007

Published:

March 20, 2008

Keywords:

nonlinear control, anytime systems, multiple models, parallel distributed compensation, aeroelastic wing section

Abstract

Nowadays in solving control problems the processing is performed typically by model-based computer systems, which contain a representation of our knowledge about the nature and the actual circumstances of the problem in hand. If the nature and/or the actual circumstances change, the corresponding model should also be changed. Anytime techniques are very flexible in this respect and can advantageously be used when the operation should be performed under changing circumstances. In this paper, a nonlinear state dependant control methodology is proposed for anytime use and as an example is applied to globally stabilize a given prototypical aeroelastic wing section via one control surface.

Cite this article as:

A. Várkonyi-Kóczy, “State Dependant Anytime Control Methodology for Non-Linear Systems,” J. Adv. Comput. Intell. Intell. Inform., Vol.12, No.2, pp. 198-205, 2008.

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References

[1] J. J. Block and T. W. Strganac, “Applied active control for nonlinear aeroelastic structure,” Journal of Guidance, Control, and Dynamics, 0731-5090, Vol.21, No.6, pp. 838-845, 1996.
[2] J. Ko, A. J. Kridula, and T. W. Strganac, “Nonlinear Control Theory for a Class of Structural Nonlinearities in a Prototypical Wing Section,” AIAA Papers 97-0580, pp. 1181-1189, 1997.
[3] T. O’Neil, H. C. Gilliat, and T. W. Strganac, “Investigations of aeroelastic response for a system with continuous structural nonlinearities,” AIAA Papers 96-1390, 1996.
[4] J. Ko, A. J. Kridula, and T. W. Strganac, “Nonlinear dynamics and control for a structurally nonlinear aeroelastic system,” AIAA Papers 97-1024, 1997.
[5] W. W. Yim, S. N. Singh, and W. R. Wells, “Nonlinear Control of a Prototypical Aeroelastic Wing Section: State Dependant Riccati equation Method,” Proc. of the Int. Conf. on Nonlinear Problems in Aviation and Aerospace, FIT, Florida, 2002.
[6] A. R. Várkonyi-Kóczy and T. Kovácsházy, “Anytime Algorithms in Embedded Signal Processing Systems,” Proc. of the IX. European Signal Processing Conference, EUSIPCO-98, Rhodes, Greece, Vol.1, pp. 169-172, Sep. 8-11, 1998.
[7] C. Baron, J.-C. Geffroy, and G. Motet (Eds.), “Embedded System Applications,” Kluwer Academic Publishers, 1997.
[8] P. Baranyi, “HOSVD based TP model transformation as a way to lmi based controller design,” IEEE Trans. on Industrial Electronics, Vol.51, No.2, pp. 387-400, April 2004.
[9] K. Tanaka and H. O. Wang, “Fuzzy Control Systems Design and Analysis,” John Wiley & Sons, Inc. New York, 2001.
[10] S. Zilberstein, “Using Anytime Algorithms in Intelligent Systems,” AI Magazine, Vol.17, No.3, pp. 73-83, 1996.
[11] A. R. Várkonyi-Kóczy, T. Kovácsházy, O. Takács, and Cs. Benedecsik, “Anytime Algorithms in Intelligent Measurement and Control,” Proc. of the 2000 World Automation Congress, WAC’2000, Maui, USA, June 11-16, 2000.
[12] A. R. Várkonyi-Kóczy, A. Ruano, P. Baranyi, and O. Takács, “Anytime Information Processing Based on Fuzzy and Neural Network Models,” Proc. of the 2001 IEEE Instrumentation and Measurement Technology Conference, IMTC/2001, Budapest, Hungary, pp. 1247-1252, May 21-23, 2001.
[13] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, “Linear Matrix Inequalities in System and Control Theory,” SIAM, Philadelphia, 1994.
[14] L. D. Lathauwer, B. D. Moor, and J. Vanderwalle, “A Multi Linear Singular Value Decomposition,” SIAM Journal on Matrix Analysis and Applications, Vol.21, No.4, pp. 1253-1278, 2000.
[15] D. Tikk, “On nowhere denseness of certain fuzzy controllers containing prerestricted number of rules,” Tatra Mountains Math. Publ., pp. 369-377, 1999.
[16] Y. C. Fung, “An Introduction to the Theory of Aeroelasticity,” John Wiley and Sons, New York, 1955.
[17] T. O’Neil and T. W. Strganac, “An Experimental Investigation of Nonlinear Aeroelastic Response,” AIAA Journal of Aircraft, Vol.35, No.4, pp. 616-622, Aug. 1998.
[18] K. Tanaka, T. Ikeda, and H. O. Wang, “Robust Stabilization of a Class of Uncertain Nonlinear Systems via Fuzzy Control: Quadratic Stabilizability, H_∞ Control Theory, and Matrix Inequalities,” IEEE Trans. on Fuzzy Systems, Vol.4, No.1, pp. 1-13, 1996.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] J. J. Block and T. W. Strganac, “Applied active control for nonlinear aeroelastic structure,” Journal of Guidance, Control, and Dynamics, 0731-5090, Vol.21, No.6, pp. 838-845, 1996.

[2] [2] J. Ko, A. J. Kridula, and T. W. Strganac, “Nonlinear Control Theory for a Class of Structural Nonlinearities in a Prototypical Wing Section,” AIAA Papers 97-0580, pp. 1181-1189, 1997.

[3] [3] T. O’Neil, H. C. Gilliat, and T. W. Strganac, “Investigations of aeroelastic response for a system with continuous structural nonlinearities,” AIAA Papers 96-1390, 1996.

[4] [4] J. Ko, A. J. Kridula, and T. W. Strganac, “Nonlinear dynamics and control for a structurally nonlinear aeroelastic system,” AIAA Papers 97-1024, 1997.

[5] [5] W. W. Yim, S. N. Singh, and W. R. Wells, “Nonlinear Control of a Prototypical Aeroelastic Wing Section: State Dependant Riccati equation Method,” Proc. of the Int. Conf. on Nonlinear Problems in Aviation and Aerospace, FIT, Florida, 2002.

[6] [6] A. R. Várkonyi-Kóczy and T. Kovácsházy, “Anytime Algorithms in Embedded Signal Processing Systems,” Proc. of the IX. European Signal Processing Conference, EUSIPCO-98, Rhodes, Greece, Vol.1, pp. 169-172, Sep. 8-11, 1998.

[7] [7] C. Baron, J.-C. Geffroy, and G. Motet (Eds.), “Embedded System Applications,” Kluwer Academic Publishers, 1997.

[8] [8] P. Baranyi, “HOSVD based TP model transformation as a way to lmi based controller design,” IEEE Trans. on Industrial Electronics, Vol.51, No.2, pp. 387-400, April 2004.

[9] [9] K. Tanaka and H. O. Wang, “Fuzzy Control Systems Design and Analysis,” John Wiley & Sons, Inc. New York, 2001.

[10] [10] S. Zilberstein, “Using Anytime Algorithms in Intelligent Systems,” AI Magazine, Vol.17, No.3, pp. 73-83, 1996.

[11] [11] A. R. Várkonyi-Kóczy, T. Kovácsházy, O. Takács, and Cs. Benedecsik, “Anytime Algorithms in Intelligent Measurement and Control,” Proc. of the 2000 World Automation Congress, WAC’2000, Maui, USA, June 11-16, 2000.

[12] [12] A. R. Várkonyi-Kóczy, A. Ruano, P. Baranyi, and O. Takács, “Anytime Information Processing Based on Fuzzy and Neural Network Models,” Proc. of the 2001 IEEE Instrumentation and Measurement Technology Conference, IMTC/2001, Budapest, Hungary, pp. 1247-1252, May 21-23, 2001.

[13] [13] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, “Linear Matrix Inequalities in System and Control Theory,” SIAM, Philadelphia, 1994.

[14] [14] L. D. Lathauwer, B. D. Moor, and J. Vanderwalle, “A Multi Linear Singular Value Decomposition,” SIAM Journal on Matrix Analysis and Applications, Vol.21, No.4, pp. 1253-1278, 2000.

[15] [15] D. Tikk, “On nowhere denseness of certain fuzzy controllers containing prerestricted number of rules,” Tatra Mountains Math. Publ., pp. 369-377, 1999.

[16] [16] Y. C. Fung, “An Introduction to the Theory of Aeroelasticity,” John Wiley and Sons, New York, 1955.

[17] [17] T. O’Neil and T. W. Strganac, “An Experimental Investigation of Nonlinear Aeroelastic Response,” AIAA Journal of Aircraft, Vol.35, No.4, pp. 616-622, Aug. 1998.

[18] [18] K. Tanaka, T. Ikeda, and H. O. Wang, “Robust Stabilization of a Class of Uncertain Nonlinear Systems via Fuzzy Control: Quadratic Stabilizability, H_∞ Control Theory, and Matrix Inequalities,” IEEE Trans. on Fuzzy Systems, Vol.4, No.1, pp. 1-13, 1996.